For vibrating strings also, null-controllability by L(p)-controls on the boundary is shown by a direct method which makes use of d'Alembert's solution formula for the wave equation.}, author = {Krabs, W. and Leugering, Günter}, doi = {10.1002/mma.1670170202}, faupublication = {no}, journal = {Mathematical Methods in the Applied Sciences}, pages = {77-93}, peerreviewed = {Yes}, title = {{ON} {BOUNDARY} {CONTROLLABILITY} {OF} {ONE}-{DIMENSIONAL} {VIBRATING} {SYSTEMS} {BY} {W}(0)1,{P}-{CONTROLS} {FOR} p∈[2, ∞]}, url = {http://onlinelibrary.wiley.com/doi/10.1002/mma.1670170202/abstract}, volume = {17}, year = {1994} } @incollection{faucris.118842284, address = {Berlin}, author = {Jahn, Johannes}, booktitle = {Recent Advances and Historical Development of Vector Optimization}, editor = {J. Jahn, W. Krabs}, faupublication = {no}, note = {UnivIS-Import:2015-04-17:Pub.1987.nat.dma.pama21.dualit}, pages = {160-172}, peerreviewed = {unknown}, publisher = {Springer}, series = {Lecture Notes in Economics and Mathematical Systems}, title = {{Duality} in {Partially} {Ordered} {Sets}}, year = {1987} } @incollection{faucris.123288264, abstract = {We compare the quality and generation performance of the optimal control sequence produced by the software frameworks BlueM.MPC and Lamatto.}, author = {Heusch, Steffen and Hild, Johannes and Leugering, Günter and Ostrowski, Manfred}, booktitle = {Mathematical Optimization of Water Networks}, doi = {10.1007/978-3-0348-0436-3_9}, editor = {Birkhäuser Basel}, faupublication = {yes}, isbn = {978-3-0348-0435-6}, pages = {151-165}, peerreviewed = {unknown}, publisher = {Springer Basel}, series = {International Series of Numerical Mathematics}, title = {{Performance} and {Comparison} of {BlueM}.{MPC} and {Lamatto}}, volume = {162}, year = {2012} } @inproceedings{faucris.107051164, abstract = {The problem of exact null controllability of normalized strings and beams subject to boundary controls in an L/sup p/(0,T)-space, where p is larger than or equal to two, is discussed. In particular, the case of L/sup infinity /-controls is of great importance in the applications. It is shown that subtle questions about Fourier series come into play in this problem. In particular, dealing with beam related control problems, lacunary Fourier series play a dominant role; this refers to the notions of (p,q)-sets. Various results on exact controllability with L/sup p/-controls of special string and beam models are given.}, author = {Leugering, Günter}, booktitle = {Decision and Control, 1990., Proceedings of the 29th IEEE Conference}, date = {1990-12-05/1990-12-07}, doi = {10.1109/CDC.1990.203793}, editor = {IEEE}, faupublication = {no}, month = {Jan}, peerreviewed = {unknown}, publisher = {IEEE Xplore}, title = {{SOME} {REMARKS} {ON} {EXACT} {CONTROLLABILITY} {OF} {STRINGS} {AND} {BEAMS} {WITH} {BOUNDARY} {CONTROLS} {IN} {LP}({O},{T}), {P}-{GREATER}-{THAN}-{OR}-{EQUAL}-{TO}-2}, url = {http://ieeexplore.ieee.org/document/203793/}, year = {1990} } @incollection{faucris.119025984, abstract = {

In active flood hazard mitigation, lateral flow withdrawal is used to reduce the impact of flood waves in rivers. Through emergency side channels, lateral outflow is generated. The optimal outflow controls the flood in such a way that the cost of the created damage is minimized. The flow is governed by a networked system of nonlinear hyperbolic partial differential equations, coupled by algebraic node conditions. Two types of integrals appear in the objective function of the corresponding optimization problem: Boundary integrals (for example, to measure the amount of water that flows out of the system into the floodplain) and distributed integrals.

For the evaluation of the derivative of the objective function, we introduce an adjoint backwards system. For the numerical solution we consider a discretized system with a consistent discretization of the continuous adjoint system, in the sense that the discrete adjoint system yields the derivatives of the discretized objective function. Numerical examples are included.

}, address = {Basel}, author = {Gugat, Martin}, booktitle = {International Series of Numerical Mathematics}, doi = {10.1007/978-3-7643-7721-2_4}, editor = {Karl-Heinz Hoffmann, Günter Leugering, Michael Hintermüller}, faupublication = {yes}, isbn = {978-3-7643-7721-2}, keywords = {St. Venant equations; subcritical states; adjoint system; optimal boundary control; necessary optimality conditions; classical solutions}, note = {UnivIS-Import:2015-04-20:Pub.2007.nat.dma.zentr.optima}, pages = {69-94}, peerreviewed = {unknown}, publisher = {Birkhäuser}, series = {Control of Coupled Partial Differential Equations}, title = {{Optimal} {Boundary} {Control} in {Flood} {Management}}, url = {http://link.springer.com/chapter/10.1007/978-3-7643-7721-2_4}, volume = {155}, year = {2007} } @article{faucris.117348924, author = {Eichfelder, Gabriele and Gugat, Martin}, faupublication = {yes}, journal = {Das Wirtschaftsstudium}, note = {UnivIS-Import:2015-03-09:Pub.2010.nat.dma.zentr.optimi}, pages = {571-578}, peerreviewed = {No}, title = {{Optimierung} mit mehreren konkurrierenden {Zielen}}, year = {2010} } @article{faucris.111690964, abstract = {This paper presents a multiobjective search algorithm with subdivision technique (MOSAST) for the global solution of multiobjective constrained optimization problems with possibly noncontinuous objective or constraint functions. This method is based on a random search method and a new version of the Graef-Younes algorithm and it uses a subdivision technique. Numerical results are given for bicriterial test problems. © 2006 Springer Science + Business Media, LLC.}, author = {Jahn, Johannes}, doi = {10.1007/s10589-006-6450-4}, faupublication = {yes}, journal = {Computational Optimization and Applications}, keywords = {Global optimization; Random search; Vector optimization}, note = {UnivIS-Import:2015-03-09:Pub.2006.nat.dma.pama21.multio}, pages = {161-175}, peerreviewed = {Yes}, title = {{Multiobjective} {Search} {Algorithm} with {Subdivision} {Technique}}, volume = {35}, year = {2006} } @phdthesis{faucris.202429588, abstract = {Numerical topology optimization based on the ersatz material model is very attractive in the research community and industry. Large scale nonlinear problems can be solved efficiently through the availability of appropriate optimizers, often resulting in non-intuitive solutions. However, topology optimization has not yet been established in the design of practical sensors and actuators. To this end we perform a thorough analysis and discussion of two exemplary piezoelectric devices, a single-frequency loudspeaker and a cantilevered energy harvester.With respect to the loudspeaker a broad range of objective functions is compared and discussed, culminating in a fully coupled piezoelectric-mechanical-acoustic near field topology optimization problem. Piezoelectric strain cancellation and acoustic short circuits need to be balanced with structural resonance in order to obtain close to resonance performance for almost arbitrary target frequencies. Providing appropriate initial designs proved to be essential for robust optimization.

Cantilevered piezoelectric energy harvesters have been subject to various optimization approaches. However these have generally been based on reduced model assumptions. We present topology optimization of a realistic cantilevered energy harvester model. It proved to be necessary to use advanced topology optimization techniques, stress constraints to enforce practically feasible designs and Heaviside filtering for void features size control and for obtaining a black and white design pattern. To the best of our knowledge, this is the first time that dynamic piezoelectric stress constraints have been formulated for topology optimization. The obtained result is mechanism-based and interpretable to manufacture. This appears to be a novel finding in the field of cantilevered piezoelectric energy harvesting design.

Performing numerical experiments, we were surprised to observe pronounced piezoelectric self-penalization, which means optimal black and white solutions without penalizing design interpolation and additional constraints beside box constraints on the design variable. This phenomenon is only rarely and briefly described in the literature. Within this thesis we perform initial heuristic steps in the analysis of the self-penalization phenomenon, which indeed appears in many different topology optimization problems. Once self-penalization is rigorously understood, our vision is to find methods supporting the self-penalizing effect and to obtain solutions potentially closer to the original problem than constrained and penalized ersatz problems. To this end we present oscillation constraints, a feature size control with independent solid and void feature size without enforcing intermediate pseudo material.

There are very few results about analytic solutions of problems of optimal control with minimal

We give the analytic solution for certain classes of target points, for example, target points that are given by constant functions. For such targets with zero velocity, the analytic solution has been given by Bennighof and Boucher in Ref. 1.

}, author = {Gugat, Martin}, doi = {10.1023/A:1016091803139}, faupublication = {no}, journal = {Journal of Optimization Theory and Applications}, keywords = {Optimal Control; Wave Equation; Analytic Solution; Distributed Parameter Systems}, note = {UnivIS-Import:2015-03-09:Pub.2002.nat.dma.lama1.analyt}, pages = {397-421}, peerreviewed = {Yes}, title = {{Analytic} {Solutions} of {L}-infinity optimal control problems for the wave equation}, volume = {114}, year = {2002} } @article{faucris.112749824, abstract = {Compressible squeeze film damping is a phenomenon of great importance for micromachines. For example, for the optimal design of an electrostatically actuated micro-cantilever mass sensor that operates in air, it is essential to have a model for the system behavior that can be evaluated efficiently. An analytical model that is based upon a solution of the linearized Reynolds equation has been given by R.B. Darling. In this paper we explain how some infinite sums that appear in Darling’s model can be evaluated analytically. As an example of applications of these closed form representations, we compute an approximation for the critical frequency where the spring component of the reaction force on the microplate, due to the motion through the air, is equal to a certain given multiple of the damping component. We also show how some double series that appear in the model can be reduced to a single infinite series that can be approximated efficiently.}, author = {Gugat, Martin}, doi = {10.3390/app2020479}, faupublication = {yes}, journal = {Applied Sciences}, keywords = {squeeze film; optimal sensor design; resonant mass sensor; double series; efficient approximation of double series; evaluation of infinite series; Darling’s model}, note = {UnivIS-Import:2015-03-09:Pub.2012.nat.dma.zentr.closed}, pages = {479-484}, peerreviewed = {unknown}, title = {{Closed} {Form} {Representations} of {Some} {Series} in {Darling}s {Model} for {Squeeze} {Film} {Damping} with a {Rectangular} {Plate}}, url = {http://www.mdpi.com/2076-3417/2/2/479}, volume = {2}, year = {2012} } @article{faucris.119966264, abstract = {
An integrodifferential equation of the Volterra type is considered under the action of an*L*_{2}(0, T, L_{2}(Γ))-boundary control. By harmonic analysis arguments it is shown that the controllability results obtained in [17] for the underlying reference model associated with a trivial convolution kernel, carry over to the model under consideration without any smallness assumption concerning the memory kernel.

}, author = {Leugering, Günter}, doi = {10.1007/BF01442653}, faupublication = {no}, journal = {Applied Mathematics and Optimization}, pages = {223-250}, peerreviewed = {Yes}, title = {{EXACT} {BOUNDARY} {CONTROLLABILITY} {OF} {AN} {INTEGRODIFFERENTIAL} {EQUATION}}, url = {http://link.springer.com/article/10.1007/BF01442653}, volume = {15}, year = {1987} } @article{faucris.112052644, abstract = {We consider a sloped canal with friction that is governed by the Saint-Venant system with source term. We show that starting sufficiently close to a stationary constant subcritical initial state, we can control the system in finite time to a state in a C

We show that certain delays in the boundary feedback preserve the exponential stability of the system. In particular, we show that the system is exponentially stable with delays freely switching between the values 4Lc and 8Lc, where L is the length of the string and c is the wave speed. © 2011 Elsevier B.V. All rights reserved.},
author = {Gugat, Martin and Tucsnak, Marius},
doi = {10.1016/j.sysconle.2011.01.004},
faupublication = {yes},
journal = {Systems & Control Letters},
keywords = {Boundary feedback; Delay; Feedback stabilization of pdes; Feedback with delay; Hyperbolic pde; Past observation; String; Switching delay; Wave equation},
note = {UnivIS-Import:2015-03-09:Pub.2011.nat.dma.zentr.anexam},
pages = {226-230},
peerreviewed = {Yes},
title = {{An} example for the switching delay feedback stabilization of an infinite dimensional system: {The} boundary stabilization of a string},
volume = {60},
year = {2011}
}
@article{faucris.215204958,
abstract = {This paper presents a new Lagrange theory of discrete-continuous conic optimization in an infinite dimensional setting. The following questions are answered for discrete-continuous optimization problems: how to define a Lagrange functional, how Karush-Kuhn-Tucker conditions look like, and which duality results can be obtained? This approach is based on new separation theorems for discrete sets, which are also given in this paper. The developed theory is finally applied to problems of discrete-continuous semidefinite and copositive optimization.},
author = {Jahn, Johannes and Knossalla, Martin},
doi = {10.23952/jnva.2.2018.3.07},
faupublication = {yes},
journal = {Journal of Nonlinear and Variational Analysis},
month = {Jan},
note = {CRIS-Team WoS Importer:2019-04-02},
pages = {317-342},
peerreviewed = {Yes},
title = {{LAGRANGE} {THEORY} {OF} {DISCRETE}-{CONTINUOUS} {NONLINEAR} {OPTIMIZATION}},
volume = {2},
year = {2018}
}
@article{faucris.110779944,
abstract = {The problem of time-optimal control of linear hyperbolic systems is equivalent to the computation of the root of the optimal value function of a time-parametric program, whose feasible set is described by a countable system of moment equations. To compute this root, discretized problems with a finite number of equality constraints can be used. In this paper, we show that on a certain time-interval, the optimal value functions of the discretized problems converge uniformly to the optimal value function of the original problem. We also give sufficient conditions for Lipschitz and Hölder continuity of the optimal value function of the original problem.},
author = {Gugat, Martin},
faupublication = {no},
journal = {Control and Cybernetics},
keywords = {Continuity; Discretization; Hölder condition; Lipschitz condition; Moment problems; Optimal value function; Parametric optimization; Time-minimal control; Uniform convergence},
note = {UnivIS-Import:2015-03-05:Pub.1999.nat.dma.zentr.timepa},
pages = {7-33},
peerreviewed = {Yes},
title = {{Time}-{Parametric} {Control}: {Uniform} {Convergence} of the optimal value functions of the discretized problems},
volume = {28},
year = {1999}
}
@article{faucris.113253404,
abstract = {In analogy to the scalarization principle in vector optimization, this paper presents a new vectorization approach for set optimization problems. Vectorization means the replacement of a set optimization problem by a suitable vector optimization problem. This approach is developed for the set less order relation used by Kuroiwa and the minmax less order relation introduced by Ha and Jahn. © 2013 Springer Science+Business Media New York.},
author = {Jahn, Johannes},
doi = {10.1007/s10957-013-0363-z},
faupublication = {yes},
journal = {Journal of Optimization Theory and Applications},
keywords = {Optimality conditions; Order relations; Scalarization; Set optimization},
note = {UnivIS-Import:2015-03-09:Pub.2013.nat.dma.pama21.vector},
pages = {783 - 795},
peerreviewed = {Yes},
title = {{Vectorization} in {Set} {Optimization}},
volume = {167},
year = {2015}
}
@article{faucris.119588304,
author = {Truong, Xuan Duc Ha and Jahn, Johannes},
faupublication = {yes},
journal = {Journal of Nonlinear and Convex Analysis},
pages = {415 - 429},
peerreviewed = {Yes},
title = {{Properties} of {Bishop}-{Phelps} cones},
volume = {18},
year = {2017}
}
@article{faucris.117908824,
abstract = {We derive a distributed-parameter model of a thin non-linear thermoelastic beam in three dimensions. The beam can also be initially curved and twisted. Our main task is to formulate the non-homogeneous initial, boundary and node value problem associated with the dynamics of a network of a finite number of such beams. The emphasis here is on a distributed-parameter modelling of the geometric and kinematic node conditions. The forces and couples appearing in the boundary and node conditions can then be viewed as control variables. The analysis of the resulting control systems and their controllability and stabilizability properties is the subject of [25] and of forthcoming papers.},
author = {Langnese, John E. and Leugering, Günter and Schmidt, E. J. P. Georg},
doi = {10.1002/mma.1670160503},
faupublication = {no},
journal = {Mathematical Methods in the Applied Sciences},
pages = {327-358},
peerreviewed = {Yes},
title = {{MODELING} {OF} {DYNAMIC} {NETWORKS} {OF} {THIN} {THERMOELASTIC} {BEAMS}},
url = {http://onlinelibrary.wiley.com/doi/10.1002/mma.1670160503/full},
volume = {16},
year = {1993}
}
@inproceedings{faucris.113999424,
author = {Rathmann, Wigand and Vogel, Frank and Landes, Hermann},
booktitle = {22. CAD-FEM Users' Meeting},
faupublication = {no},
peerreviewed = {No},
publisher = {CAD-FEM GmbH Grafing},
title = {{Numerical} {Optimization} of {Time}-dependent {Electromechanical} {Systems}},
year = {2004}
}
@inproceedings{faucris.121306504,
abstract = {This paper aims at identifying appropriate bottom anti-reflective coatings (BARCs) for double patterning techniques such as Litho-Freeze-Litho-Etch (LFLE). A short introduction into the employed optimization methodology, including variables, figures of merit, models and optimization algorithms is given. A study on the impact of a refractive index modulation caused by the first lithographic step is presented. Several optimization surveys taking the index modulation into account are set forth, and the results are discussed. In addition to optimization procedures aiming at optimizing one litho step at a time, a co-optimization study for both litho steps is proposed. Finally, two multi-objective optimization procedures that allow for a post-optimization exploration and selection of optimum solutions are presented. Numerous solutions are discussed in terms of their anti-reflectance behavior and their manufacturing feasibility. © 2010 SPIE.},
author = {Jahn, Johannes and Erdmann, Andreas and Fühner, Tim and Liu, S. and Shao, F. and Barenbaum, A.},
booktitle = {Proceedings of the SPIE},
date = {2010-02-23/2010-02-25},
doi = {10.1117/12.846441},
faupublication = {yes},
keywords = {bottom anti-reflective coating (BARC); double patterning; lithography simulation; waferstack optimization},
note = {UnivIS-Import:2015-04-16:Pub.2010.nat.dma.pama21.topogr},
pages = {76403C},
peerreviewed = {unknown},
publisher = {SPIE},
title = {{Topography}-aware {BARC} optimization for double patterning},
venue = {San Jose},
volume = {7640},
year = {2010}
}
@misc{faucris.118869344,
abstract = {We consider nonlinear and nonsmooth mixing aspects in gas transport
optimization problems. As mixed-integer reformulations of pooling-type
mixing models already render small-size instances computationally
intractable, we investigate the applicability of smooth nonlinear
programming techniques for equivalent complementarity-based
reformulations. Based on recent results for remodeling piecewise affine
constraints using an inverse parametric quadratic programming approach,
we show that classical stationarity concepts are meaningful for the
resulting complementarity-based reformulation of the mixing equations.
Further, we investigate in a numerical study the performance of this
reformulation compared to a more compact complementarity-based one that
does not feature such beneficial regularity properties. All computations
are performed on publicly available data of real-world size problem
instances from steady-state gas transport.},
author = {Hante, Falk and Schmidt, Martin},
faupublication = {yes},
keywords = {Gas transport networks, Mixing, Inverse parametric quadratic programming, Complementarity constraints, MPCC},
peerreviewed = {automatic},
title = {{Complementarity}-{Based} {Nonlinear} {Programming} {Techniques} for {Optimal} {Mixing} in {Gas} {Networks}},
url = {http://www.optimization-online.org/DB_HTML/2017/09/6198.html},
year = {2017}
}
@article{faucris.122593064,
abstract = {The paper concerns the analysis of equilibrium problems for 2D elastic bodies with thin inclusions modeled in the framework of Timoshenko beams. The first focus is on the well-posedness of the model problem in a variational setting. Then delaminations of the inclusions are considered, forming a crack between the elastic body and the inclusion. Nonlinear boundary conditions at the crack faces are considered to prevent a mutual penetration between the faces. The corresponding variational formulations together with weak and strong solutions are discussed. The model contains various physical parameters characterizing the mechanical properties of the inclusion, such as flexural and shear stiffness. The paper provides an asymptotic analysis of such parameters. It is proved that in the limit cases corresponding to infinite and zero rigidity, we obtain rigid inclusions and cracks with the non-penetration conditions, respectively. Finally, exemplary networks of Timoshenko beams are considered as inclusions as well.},
author = {Khludnev, A. M. and Leugering, Günter},
doi = {10.1177/1081286513505106},
faupublication = {yes},
journal = {Mathematics and Mechanics of Solids},
keywords = {Thin elastic inclusion;Timoshenko beams;crack;delamination;non-penetration boundary condition},
pages = {495-511},
peerreviewed = {Yes},
title = {{On} {Timoshenko} thin elastic inclusions inside elastic bodies},
volume = {20},
year = {2015}
}
@article{faucris.121409464,
author = {Jahn, Johannes},
faupublication = {no},
journal = {Optimization},
note = {UnivIS-Import:2015-03-05:Pub.1983.nat.dma.pama21.zurvek},
pages = {577-591},
peerreviewed = {Yes},
title = {{Zur} vektoriellen linearen {Tschebyscheff}-{Approximation}},
volume = {14},
year = {1983}
}
@book{faucris.123698784,
abstract = {We consider optimal control problems for elliptic systems under control constraints on networked domains. In particular, we study such systems in a format that allows for applications in problems including membranes and Reissner-Mindlin plates on multi-link-domains, called networks. We first provide the models, derive first order optimality conditions in terms of variational equations and inequalities for a control-constrained linear-quadratic optimal control problem, and then introduce a non-overlapping iterative domain decomposition method, which is based on Robin-type interface updates at multiple joints (edges). We prove convergence of the iteration and derive a posteriori error estimates with respect to the iteration across the interfaces.},
author = {Leugering, Günter},
doi = {10.1007/978-3-540-75199-1_10},
faupublication = {yes},
isbn = {9783540751984},
pages = {119-130},
peerreviewed = {unknown},
title = {{Domain} decomposition of constrained optimal control problems for 2d elliptic system on networked domains: convergence and a posteriori error estimates},
volume = {60},
year = {2008}
}
@article{faucris.107372804,
abstract = {In these notes we consider PDE-constrained optimization in the context of advanced materials. We give examples for optimization and control in the coefficients, free material optimization, topology optimization, shape optimization in elastic and piezo-electric materials. We explain some approaches to metamaterials, in particular for auxetic materials},
author = {Leugering, Günter and Stingl, Michael},
doi = {10.1002/gamm.201010016},
faupublication = {yes},
journal = {GAMM-Mitteilungen},
keywords = {piezoelectricity; electromechanical interaction; shape sensitivity analysis},
pages = {209-229},
peerreviewed = {unknown},
title = {{PDE}-constrained optimization for advanced materials},
url = {http://onlinelibrary.wiley.com/doi/10.1002/gamm.201010016/epdf},
volume = {33},
year = {2010}
}
@article{faucris.110282524,
abstract = {In this paper an interior point method is presented for nonlinear programming problems with inequality constraints. On defining a modified distance function the original problem is solved sequentially by using a method of feasible directions. At each iteration a usable feasible direction can be determined explicitly. Under certain assumptions it can be shown that every accumulation point of the sequence of points constructed by the proposed algorithm satisfies the Kuhn-Tucker conditions. © 1979 Physica-Verlag.},
author = {Jahn, Johannes},
doi = {10.1007/BF01917332},
faupublication = {no},
journal = {Mathematical Methods of Operations Research},
note = {UnivIS-Import:2015-03-05:Pub.1979.nat.dma.pama21.aninte},
pages = {1-15},
peerreviewed = {Yes},
title = {{An} {Interior} {Point} {Method} for {Nonlinear} {Programming}},
volume = {23},
year = {1979}
}
@article{faucris.123273084,
abstract = {We investigate the propagation of cracks in 2-d elastic domains, which are subjected to quasi-static loading scenarios. As we take cohesive effects along the crack path into account and impose a non-penetration condition, inequalities appear in the constitutive equations describing the elastic behavior of a domain with crack. In contrast to existing approaches, we consider cohesive effects arising from crack opening in normal as well as in tangential direction. We establish a constrained energy minimization problem and show that the solution of this problem satisfies the set of constitutive equations. In order to solve the energy minimization problem numerically, we apply a finite element discretization using a combination of standard continuous finite elements with so-called cohesive elements. A particular strength of our method is that the crack path is a result of the minimization process. We conclude the article by numerical experiments and compare our results to results given in the literature.},
author = {Prechtel, Marina and Leugering, Günter and Steinmann, Paul and Stingl, Michael},
doi = {10.3934/cpaa.2013.12.1705},
faupublication = {yes},
journal = {Communications on Pure and Applied Analysis},
keywords = {Energy minimization; cohesive elements; crack problems.},
pages = {1705-1729},
peerreviewed = {Yes},
title = {{A} cohesive crack propagation model: {Mathematical} theory and numerical solution},
volume = {12},
year = {2013}
}
@article{faucris.120845164,
author = {Hante, Falk and Amin, Saurabh and Bayen, Alexandre M.},
doi = {10.1109/TAC.2011.2158171},
faupublication = {no},
journal = {IEEETransactions on Automatic Control},
pages = {291--301},
peerreviewed = {Yes},
title = {{Exponential} stability of switched linear hyperbolic initial-boundary value problems},
volume = {57},
year = {2012}
}
@article{faucris.110289344,
abstract = {For a system that is governed by the isothermal Euler equations with friction for ideal gas, the corresponding field of characteristic curves is determined by the velocity of the flow. This velocity is determined by a second-order quasilinear hyperbolic equation. For the corresponding initial-boundary value problem with Neumann-boundary feedback, we consider non-stationary solutions locally around a stationary state on a finite time interval and discuss the well-posedness of this kind of problem. We introduce a strict H2-Lyapunov function and show that the boundary feedback constant can be chosen such that the H2-Lyapunov function and hence also the H2-norm of the difference between the non-stationary and the stationary state decays exponentially with tim},
author = {Gugat, Martin and Leugering, Günter and Wang, Ke},
doi = {10.3934/mcrf.2017015},
faupublication = {yes},
journal = {Mathematical Control and Related Fields},
keywords = {Boundary feedback control, feedback stabilization, exponential stability, isothermal Euler equations, second-order quasilinear equation, Lyapunov function, stationary state, non-stationary state, gas pipeline},
pages = {419 - 448},
peerreviewed = {Yes},
title = {{Neumann} boundary feedback stabilization for a nonlinear wave equation: {A} strict {H2}-{Lyapunov} function},
volume = {7},
year = {2017}
}
@article{faucris.108502284,
author = {Jahn, Johannes},
faupublication = {yes},
journal = {Journal of Optimization Theory and Applications},
pages = {707-725},
peerreviewed = {Yes},
title = {{Karush}-{Kuhn}-{Tucker} {Conditions} in {Set} {Optimization}},
volume = {172},
year = {2017}
}
@incollection{faucris.122683924,
abstract = {The purpose of this paper is to disduss, in a fairly heuristic way, certain aspects of modelling and controllability of flexible, multi-beam structures from the point of view of local modelling of the structure by distributed parameter systems.},
address = {Berlin, Heidelberg},
author = {Langnese, John E. and Leugering, Günter and Schmidt, E. J. P. Georg},
booktitle = {System Modelling and Optimization - Proceedings of the 15th IFIP Conference Zurich, Switzerland, September 2–6, 1991},
doi = {10.1007/BFb0113314},
editor = {L.D. Davisson; A.G.J. MacFarlane; H. Kwakernaak; J.L. Massey; Ya Z. Tsypkin; A.J. Viterbi; Peter Kall},
faupublication = {no},
isbn = {978-3-540-47220-9},
month = {Jan},
pages = {467-480},
peerreviewed = {unknown},
publisher = {New York; Springer; 1999},
series = {Lecture Notes in Control and Information Sciences},
title = {{MODELING} {AND} {CONTROLLABILITY} {OF} {NETWORKS} {OF} {THIN} {BEAMS}},
url = {http://link.springer.com/chapter/10.1007/BFb0113314},
volume = {180},
year = {1992}
}
@article{faucris.106690364,
author = {Hante, Falk and Sigalotti, Mario and Tucsnak, Marius},
doi = {10.1016/j.jde.2012.01.037},
faupublication = {no},
journal = {Journal of Differential Equations},
pages = {5569--5593},
peerreviewed = {Yes},
title = {{On} conditions for asymptotic stability of dissipative infinite-dimensional systems with intermittent damping},
volume = {252},
year = {2012}
}
@article{faucris.123049784,
abstract = {A viscoelastic liquid confined between two parallel plates is considered under the action of *L*_{2} (*O, T*)-boundary controls. Applying Laplace-Transform-techniques it is shown that *L*_{2} (*O, l*)-states are exactly controllable in finite time, depending on the speed of propagation of singularities. Finally the existence of time-optimal controls respecting a given norm bound is shown.},
author = {Leugering, Günter},
doi = {10.1002/mma.1670090130},
faupublication = {no},
journal = {Mathematical Methods in the Applied Sciences},
month = {Jan},
pages = {413-430},
peerreviewed = {Yes},
title = {{TIME} {OPTIMAL} {BOUNDARY} {CONTROLLABILITY} {OF} {A} {SIMPLE} {LINEAR} {VISCOELASTIC} {LIQUID}},
url = {http://onlinelibrary.wiley.com/doi/10.1002/mma.1670090130/full},
volume = {9},
year = {1987}
}
@article{faucris.108612284,
abstract = {Congrès

International conference on control of distributed parameter systems. 4 (1988)

1989, vol. 91, pp. 249-261 (12 ref.)},
author = {Leugering, Günter},
faupublication = {no},
journal = {International Series of Numerical Mathematics},
month = {Jan},
pages = {249-261},
peerreviewed = {unknown},
title = {{ON} {THE} {REACHABILITY} {PROBLEM} {OF} {A} {VISCOELASTIC} {BEAM} {DURING} {A} {SLEWING} {MANEUVER}},
volume = {91},
year = {1989}
}
@inproceedings{faucris.106690584,
author = {Hante, Falk and Sigalotti, Mario},
booktitle = {Decision and Control (CDC) 2010. CDC 2010, 49th IEEE Conference on},
faupublication = {no},
pages = {5668--5673},
peerreviewed = {unknown},
title = {{Existence} of common {Lyapunov} functions for infinite-dimensional switched linear systems},
year = {2010}
}
@article{faucris.116673304,
abstract = {

`We consider models based on conservation laws. For the optimization of`

`such systems, a sensitivity analysis is essential to determine how changes in the decision`

`variables influence the objective function. Here we study the sensitivity with respect`

`to the initial data of objective functions that depend upon the solution of Riemann`

`problems with piecewise linear flux functions. We present representations for the one–`

`sided directional derivatives of the objective functions. The results can be used in the`

`numerical method called Front-Tracking.`

For master students of the process technology and energy technology we offer a course on simulation of transport processes. Two aims are focused:

The students should learn or repeat the basics in using a simulation tools.

They should learn to combine specialized knowledge with mathematical concepts to simulate a technical process.

In the first part of the course the students collect first experiences in programming by modeling a Rankine cycle using Matlab. Hereby they discuss the quality of the presented mathematical model and possible improvements. The students are accompanied by the lecturers of the lecture "Transport processes" (master studies) and “Mathematics for Engineers” (bachelor studies). While working on the computer learners can discuss their questions, programming ideas and difficulties with each other and the trainers and they receive immediate feedbacks. The second part of the course is focuses on simple heat transfer processes described by ODE or PDE models. Therefore some mathematical concepts (e.g. linear equation systems) are needed, but they have learned it about three years ago.

Up to now the mathematical models of the technical processes and the repetition of the mathematical basics were presented as talks during the lectures with little time remained for the discussion. But the students need enough time to reconsider the introduced topics. We have seen, that this process needs more time then scheduled, e.g. to understand the way to describe the first derivative of a function on a interval by a system of linear equation system.

Now we are working on a didactic reorganization (flipped classroom) of our course, so that the students will have enough time, to repeat subjects needed in our course.

Therefore on-line learning modules and formative on-line tests have to be finished to prepare the single sessions. Thus questions can be discussed quite early and it remains more time to discuss, e.g. improvements of the models. By using the flipped classroom concept the students will be motivated to work more independently and they may reach a better understanding by using the digital learning materials as starting point for the considerations. Thus we will generate a more active participation in the teaching and learning events and better learner’s results can be achieved.

In my talk I would like to discuss these ideas and I will give a short status report of the actual course.

}, author = {Rathmann, Wigand and Wensing, Michael and Zepf, Stefanie}, booktitle = {The 18th SEFI Mathematics working Group Seminar}, date = {2016-06-27/2016-06-29}, faupublication = {yes}, peerreviewed = {unknown}, title = {{Flipped} classroom in interdisciplinary course}, url = {http://www.math.chalmers.se/SEFIMWG2016/Book%20of%20accepted%20abstracts/part49.htm}, venue = {Gothenburg}, year = {2016} } @incollection{faucris.106876264, author = {Jahn, Johannes}, booktitle = {Operations Research Verfahren}, faupublication = {no}, note = {UnivIS-Import:2015-03-05:Pub.1979.nat.dma.pama21.zursta}, pages = {209-215}, peerreviewed = {unknown}, title = {{Zur} {Stabilität} von {Regressionskoeffizienten}}, volume = {33}, year = {1979} } @article{faucris.107336064, abstract = {The production of nanoscaled particulate products with exactly pre-defined characteristics is of enormous economic relevance. Although there are different particle formation routes they may all be described by one class of equations. Therefore, simulating such processes comprises the solution of nonlinear, hyperbolic integro-partial differential equations. In our project we aim to study this class of equations in order to develop efficient tools for the identification of optimal process conditions to achieve desired product properties. This objective is approached by a joint effort of the mathematics and the engineering faculty. Two model-processes are chosen for this study, namely a precipitation process and an innovative aerosol process allowing for a precise control of residence time and temperature. Since the overall problem is far too complex to be solved directly a hierarchical sequence of simplified problems has been derived which are solved consecutively. In particular, the simulation results are finally subject to comparison with experiments.}, author = {Gröschel, Michael and Leugering, Günter and Peukert, Wolfgang}, doi = {10.1007/978-3-0348-0133-1_28}, faupublication = {yes}, journal = {International Series of Numerical Mathematics}, keywords = {Population balance equations; optimal control; model reduction; parameter identification}, pages = {541-559}, peerreviewed = {Yes}, title = {{Model} {Reduction}, {Structure}-property {Relations} and {Optimization} {Techniques} for the {Production} of {Nanoscale} {Particles}}, url = {http://link.springer.com/chapter/10.1007%2F978-3-0348-0133-1_28}, year = {2011} } @article{faucris.112679424, abstract = {We consider a water distribution network where at a finite number of nodes, contaminant injection can occur. We consider the problem of the identification of the contaminations. This problem can be considered as an optimal control problem with a networked system that is governed by a transport reaction equation. The identification is based upon observations from a finite number of sensors. The corresponding infinite-dimensional optimization problem is defined in a Hilbert space setting. In order to guarantee that our optimization problem has a unique solution, a quadratic regularization term is added in the objective function. Under certain assumptions on the relations of the travel times through the pipes we obtain a representation of this optimization problem that allows the computation of the solution on a discrete time grid by solving finite-dimensional linear least squares problems. On these time grids, there is no discretization error since our approach is based upon an exact representation of the system state. This is useful to minimize potential impacts of contamination emergencies on consumers by helping to select locations to flush the contaminant out of the distribution network. © 2012 Society for Industrial and Applied Mathematics.}, author = {Gugat, Martin}, doi = {10.1137/110859269}, faupublication = {yes}, journal = {SIAM Journal on Applied Mathematics}, keywords = {Contamination emergency; Hyperbolic PDE; Identification; Least squares; Network; Network dynamics; Observation; Optimal control; PDE-constrained optimization; Transport reaction equation}, note = {UnivIS-Import:2015-03-09:Pub.2012.nat.dma.lama1.contam}, pages = {1772-1791}, peerreviewed = {Yes}, title = {{Contamination} {Source} {Determination} in {Water} {Distribution} {Networks}}, url = {http://epubs.siam.org/doi/abs/10.1137/110859269}, volume = {72}, year = {2012} } @incollection{faucris.117910584, abstract = {A decomposition-method introduced in [Le1] is used to decompose the rigid-body motion from the elastic vibration of a slowly rotating beam. On the base of the transformed system, a controller is constructed that steers all oscillations of the beam to rest in finite time. In addition, the beam is thereby driven to zero angular velocity. A second result is concerned with strong feed-back stabilizability.}, address = {Berlin; Heidelberg}, author = {Leugering, Günter}, booktitle = {Optimal Control of Partial Differential Equations - Proceedings of the IFIP WG 7.2 International Conference Irsee, April 9–12, 1990}, doi = {10.1007/BFb0043223}, editor = {Prof. Karl-Heinz Hoffmann; Prof. Werner Krabs}, faupublication = {no}, isbn = {978-3-540-46883-7}, month = {Jan}, pages = {182-191}, peerreviewed = {unknown}, publisher = {New York; Springer; 1999}, series = {Lecture Notes in Control and Information Sciences}, title = {{ON} {CONTROL} {AND} {STABILIZATION} {OF} {A} {ROTATING} {BEAM} {BY} {APPLYING} {MOMENTS} {AT} {THE} {BASE} {ONLY}}, url = {http://link.springer.com/chapter/10.1007/BFb0043223}, volume = {149}, year = {1991} } @article{faucris.120147984, abstract = {This paper works out connections between semidefinite optimization and vector optimization. It is shown that well-known semidefinite optimization problems are scalarized versions of a general vector optimization problem. This scalarization leads to the minimization of the trace or the maximal eigenvalue. © Taru Publications.}, author = {Jahn, Johannes and Carosi, L. and Martein, L.}, doi = {10.1080/09720502.2003.10700341}, faupublication = {yes}, journal = {Journal of Interdisciplinary Mathematics}, note = {UnivIS-Import:2015-03-09:Pub.2003.nat.dma.pama21.xxx}, pages = {219-229}, peerreviewed = {unknown}, title = {{On} the {Connections} between {Semidefinite} {Optimization} and {Vector} {Optimization}}, volume = {6}, year = {2003} } @misc{faucris.110459844, author = {Jahn, Johannes}, faupublication = {yes}, note = {UnivIS-Import:2015-03-05:Pub.1995.nat.dma.pama21.angewa}, peerreviewed = {automatic}, title = {{Angewandte} nichtlineare {Vektoroptimierung}}, year = {1995} } @article{faucris.115105144, abstract = {In this paper the problem dual to a convex vector optimization problem is defined. Under suitable assumptions, a weak, strong and strict converse duality theorem are proved. In the case of linear mappings the formulation of the dual is refined such that well-known dual problems of Gale, Kuhn and Tucker [8] and Isermann [12] are generalized by this approach. © 1983 The Mathematical Programming Society, Inc.}, author = {Jahn, Johannes}, doi = {10.1007/BF02594784}, faupublication = {no}, journal = {Mathematical Programming}, keywords = {Duality; Vector Optimization}, note = {UnivIS-Import:2015-03-05:Pub.1983.nat.dma.pama21.dualit}, pages = {343-353}, peerreviewed = {Yes}, title = {{Duality} in {Vector} {Optimization}}, volume = {25}, year = {1983} } @article{faucris.114041664, author = {Rathmann, Wigand and Krug, Andreas}, faupublication = {no}, journal = {Infoplaner}, pages = {36--37}, peerreviewed = {No}, title = {{Grundlagen} {FEM}: {Finite}-{Differenzen}-{Verfahren}}, year = {2004} } @article{faucris.113909884, abstract = {We consider the problem to control a vibrating string to rest in a given finite time. The string is fixed at one end and controlled by Neumann boundary control at the other end. We give an explicit representation of the
We consider a vibrating string that is fixed at one end with Neumann control action at the other end. We investigate the optimal control problem of steering this system from given initial data to rest, in time T, by minimizing an objective functional that is the convex sum of the L^{2}-norm of the control and of a boundary Neumann tracking term.

We provide an explicit solution of this optimal control problem, showing that if the weight of the tracking term is positive, then the optimal control action is concentrated at the beginning and at the end of the time interval, and in-between it decays exponentially. We show that the optimal control can actually be written in that case as the sum of an exponentially decaying term and of an exponentially increasing term. This implies that, if the time T is large, then the optimal trajectory approximately consists of three arcs, where the first and the third short-time arcs are transient arcs, and in the middle arc the optimal control and the corresponding state are exponentially close to 0. This is an example of a turnpike phenomenon for a problem of optimal boundary control. If T=+∞ (infinite time horizon problem), then only the exponentially decaying component of the control remains, and the norms of the optimal control action and of the optimal state decay exponentially in time. In contrast to this situation, if the weight of the tracking term is zero and only the control cost is minimized, then the optimal control is distributed uniformly along the whole interval [0,T] and coincides with the control given by the Hilbert Uniqueness Method.

In addition, we establish a similarity theorem stating that, for every T>0, there exists an appropriate weight λ<1 for which the optimal solutions of the corresponding finite horizon optimal control problem and of the infinite horizon optimal control problem coincide along the first part of the time interval [0,2]. We also discuss the turnpike phenomenon from the perspective of a general framework with a strongly continuous semi-group.

}, author = {Gugat, Martin and Trelat, Emmanuel and ZuaZua, Enrique}, doi = {10.1016/j.sysconle.2016.02.001}, faupublication = {yes}, journal = {Systems & Control Letters}, keywords = {Vibrating string; Neumann boundary control; Turnpike phenomenon; Exponential stability; Energy decay; Exact control; Infinite horizon optimal control; Similarity theorem; Receding horizon}, pages = {61-70}, peerreviewed = {Yes}, title = {{Optimal} {Neumann} control for the {1D} wave equation: {Finite} horizon, infinite horizon, boundary tracking terms and the turnpike property}, volume = {90}, year = {2016} } @article{faucris.115106024, abstract = {In this paper several kinds of optima of a vector optimization problem are investigated; these are minimal, weakly minimal, strongly minimal and properly minimal solutions. For these optima various optimality conditions resulting from a scalarization approach are presented. Furthermore some numerical aspects are discussed. © 1985 Springer-Verlag.}, author = {Jahn, Johannes}, doi = {10.1007/BF01719756}, faupublication = {no}, journal = {Or Spectrum}, note = {UnivIS-Import:2015-03-05:Pub.1985.nat.dma.pama21.somech}, pages = {7-17}, peerreviewed = {Yes}, title = {{Some} {Characterizations} of the {Optimal} {Solutions} of a {Vector} {Optimization} {Problem}}, volume = {7}, year = {1985} } @book{faucris.118373464, address = {Aachen}, author = {Jahn, Johannes}, faupublication = {yes}, note = {UnivIS-Import:2015-04-02:Pub.2006.nat.dma.pama21.aufgab}, pages = {132}, publisher = {Shaker}, title = {{Aufgabensammlung} zur {Ingenieurmathematik}}, year = {2006} } @article{faucris.118517124, abstract = {In this contribution the identification of new reaction conditions for the production of nearly monodisperse silicon nanoparticles via the pyrolysis of monosilane in a hot wall reactor is considered. For this purpose a full finite volume model has been combined with a state-of-the-art trust-region optimisation algorithm for process control. Verified against experimental data, specific process conditions are determined accomplishing a versatile range of prescribed product properties. The main achievement of the optimisation is the possibility to control the different mechanisms in the particle formation process by mainly adjusting the temperature profile. Due to a successful separation of the nucleation and growth process, significantly narrower particle size distributions are obtained. Moreover, the presented optimisation framework establishes rate constants based on measured data.}, author = {Gröschel, Michael and Koermer, Richard and Walther, Maximilian and Leugering, Günter and Peukert, Wolfgang}, doi = {10.1016/j.ces.2012.01.035}, faupublication = {yes}, journal = {Chemical Engineering Science}, pages = {181--194}, peerreviewed = {Yes}, title = {{Process} control strategies for the gas phase synthesis of silicon nanoparticles}, volume = {73}, year = {2012} } @article{faucris.121355564, author = {Hopfgartner, Christian and Scholz, Ingo and Gugat, Martin and Leugering, Günter and Hornegger, Joachim}, faupublication = {yes}, journal = {ICGST International Journal on Graphics, Vision and Image Processing}, pages = {27-37}, peerreviewed = {unknown}, title = {{Intensity}-based 3-{D} {Reconstruction} with {Non}-linear {Optimization}}, url = {http://www5.informatik.uni-erlangen.de/Forschung/Publikationen/2010/Hopfgartner10-IRW.pdf}, volume = {10.0}, year = {2010} } @article{faucris.110561484, abstract = {We consider a countable family of one-parameter convex programs and give sufficient conditions for the one-sided differentiability of its optimal value function. The analysis is based on the Borwein dual problem for a family of convex programs (a convex disjunctive program). We give conditions that assure stability of the situation of perfect duality in the Borwein theory. For the reader's convenience, we start with a review of duality results for families of convex programs. A parametric family of dual problems is introduced that contains the dual problems of Balas and Borwein as special cases. In addition, a vector optimization problem is defined as a dual problem. This generalizes a result by Helbig about families of linear programs.}, author = {Gugat, Martin}, faupublication = {no}, journal = {Journal of Optimization Theory and Applications}, keywords = {Disjunctive programming; Efficiency; Families of convex programs; Mixed integer programming; Optimal value function; Parameteric family of dual problems; Sensitivity}, note = {UnivIS-Import:2015-03-05:Pub.1997.nat.dma.lama1.parame}, pages = {285-310}, peerreviewed = {Yes}, title = {{Parametric} {Disjunctive} {Programming}: {One}-{Sided} {Differentiability} of the {Value} {Function}}, volume = {92}, year = {1997} } @article{faucris.107390184, abstract = {We prove the Eshelby theorem for an ellipsoidal piezoelectric inclusion in an infinite piezoelectric material. Explicit formulas for the link and polarization matrices are derived. Passing to the limits with respect to parameters in the corresponding equations, the result is extended to cases when either the inclusion or the surrounding material is purely elastic.}, author = {Leugering, Günter and Nazarov, S. A.}, doi = {10.1007/s00205-014-0803-4}, faupublication = {yes}, journal = {Archive for Rational Mechanics and Analysis}, pages = {n/a}, peerreviewed = {Yes}, title = {{The} {Eshelby} {Theorem} and its {Variants} for {Piezoelectric} {Media}}, year = {2014} } @incollection{faucris.117911464, abstract = {We consider a planar graph representative of the reference configuration of a network of elastic prestretched strings coupled at the vertices of that graph. Some or all of the vertices may carry a point mass, and at those nodes dry friction on the plane may occur. We briefly describe the model and some results on well-posedness and control of such systems obtained in the literature. We then introduce a dynamic domain decomposition based on a Steklov-Poincaré-type operator. The analysis is given for the time-domain and the frequency-domain. Optimal control and problems of exact controllability are formulated and investigated in terms of the decoupling procedure.}, address = {Basel}, author = {Leugering, Günter}, booktitle = {Control and Estimation of Distributed Parameter Systems - International Conference in Vorau, Austria, July 14-20, 1996}, doi = {10.1007/978-3-0348-8849-3_15}, editor = {W. Desch; F. Kappel; K. Kunisch}, faupublication = {no}, isbn = {978-3-0348-8849-3}, keywords = {dynamic domain decomposition;strings;networks;joint masses;dry friction;Steklov-Poincare-operators for networks;differential-delay systems;optimal control;controllability; 93C20; 93C80; 93B05; 65N55}, month = {Jan}, pages = {191-205}, peerreviewed = {unknown}, publisher = {Birkhäuser}, series = {International Series of Numerical Mathematics}, title = {{On} dynamic domain decomposition of controlled networks of elastic strings and joint-masses}, url = {http://link.springer.com/chapter/10.1007/978-3-0348-8849-3_15}, volume = {126}, year = {1998} } @article{faucris.110992904, abstract = {
We consider *L* ^{∞}-norm minimal controllability problems for vibrating systems. In the common method of modal truncation controllability constraints are first reformulated as an infinite sequence of moment equations, which is then truncated to a finite set of equations. Thus, feasible controls are represented as solutions of moment problems.

In this paper, we propose a different approach, namely to replace the sequence of moment equations by a sequence of moment inequalities. In this way, the feasible set is enlarged. If a certain relaxation parameter tends to zero, the enlarged sets approach the original feasible set. Numerical examples illustrate the advantages of this new approach compared with the classical method of moments.

The introduction of moment inequalities can be seen as a regularization method, that can be used to avoid oscillatory effects. This regularizing effect follows from the fact that for each relaxation parameter, the whole sequence of eigenfrequencies is taken into account, whereas in the method of modal truncation, only a finite number of frequencies is considered.

}, author = {Gugat, Martin and Leugering, Günter}, doi = {10.1023/A:1015472323967}, faupublication = {no}, journal = {Computational Optimization and Applications}, keywords = {optimal control; exact controllability; eigenvalues; moment problem; moment inequalities; numerical algorithm; convergence}, note = {UnivIS-Import:2015-03-09:Pub.2002.nat.dma.lama1.regula}, pages = {151-192}, peerreviewed = {Yes}, title = {{Regularization} of {L}-∞ optimal control problems for distributed parameter systems}, url = {http://link.springer.com/article/10.1023/A:1015472323967}, volume = {22}, year = {2002} } @article{faucris.117901784, abstract = {We consider optimal control problems related to exact- and approximate controllability of dynamic networks of elastic strings. In this note we concentrate on problems with linear dynamics, no state and no control constraints. The emphasis is on approximating target states and velocities in part of the network using a dynamic domain decomposition method (d(3)m) for the optimality system on the network. The decomposition is established via a Uzawa-type saddle-point iteration associated with an augmented Lagrangian relaxation of the transmission conditions at multiple joints. We consider various cost functions and prove convergence of the infinite dimensional scheme for an exemplaric choice of the cost. We also give numerical evidence in the case of simple exemplaric networks.}, author = {Leugering, Günter}, doi = {10.1023/A:1008721402512}, faupublication = {yes}, journal = {Computational Optimization and Applications}, keywords = {dynamic networks of elastic strings;dynamic domain decomposition;optimal control}, pages = {5-27}, peerreviewed = {Yes}, title = {{Domain} decomposition of optimal control problems for dynamic networks of elastic strings}, url = {http://link.springer.com/article/10.1023/A:1008721402512}, volume = {16}, year = {2000} } @incollection{faucris.111077384, abstract = {In this review article the theoretical foundations for shape-topological sensitivity analysis of elastic energy functional in bodies with nonlinear cracks and inclusions are presented. The results obtained can be used to determine the location and the shape of inclusions which influence in a desirable way the energy release at the crack tip. In contrast to the linear theory, where in principle, crack lips may mutually penetrate, here we employ nonlinear elliptic boundary value problems in non-smooth domains with cracks with non-penetration contact conditions across the crack lips or faces. A shape-topological sensitivity analysis of the associated variational inequalities is performed for the elastic energy functional. Topological derivatives of integral shape functionals for variational inequalities with unilateral boundary conditions are derived. The closed form results are obtained for the Laplacian and linear elasticity in two and three spatial dimensions. Singular geometrical perturbations in the form of cavities or inclusions are considered. In the variational context the singular perturbations are replaced by regular perturbations of bilinear forms. The obtained expressions for topological derivatives are useful in numerical method of shape optimization for contact problems as well as in passive control of crack propagation.}, author = {Leugering, Günter and Sokolowski, Jan and Zochowski, Antoni}, booktitle = {Shape- and Topology Optimization for Passive Control of Crack Propagation - New Trends in Shape Optimization}, doi = {10.1007/978-3-319-17563-8_7}, editor = {Aldo Pratelli; Günter Leugering}, faupublication = {yes}, isbn = {978-3-319-17563-8}, keywords = {Frictionless contact;Elastic bodies with cracks;Signorini conditions on cracks;Variational inequality;Shape functional;Shape sensitivity;Topological sensitivity;Domain decomposition;Steklov-Poincare operator;Contact problems}, month = {Jan}, pages = {141-197}, peerreviewed = {unknown}, publisher = {Springer International Publishing}, series = {International Series of Numerical Mathematics}, title = {{Shape}- and {Topology} {Optimization} for {Passive} {Control} of {Crack} {Propagation}}, url = {http://link.springer.com/chapter/10.1007/978-3-319-17563-8_7}, volume = {166}, year = {2015} } @article{faucris.111266144, author = {Gugat, Martin}, faupublication = {yes}, journal = {Advanced Modeling and Optimization}, note = {UnivIS-Import:2015-03-09:Pub.2005.nat.dma.zentr.optima}, pages = {9-37}, peerreviewed = {unknown}, title = {{Optimal} {Control} of {Networked} {Hyperbolic} {Systems}: {Evaluation} of {Derivatives}}, url = {http://www.ici.ro/camo/journal/v7n1.htm}, volume = {7}, year = {2005} } @article{faucris.107052264, abstract = {We consider a boundary optimal control problem for the Maxwell system with a final value cost criterion. We introduce a time domain decomposition procedure for the corresponding optimality system which leads to a sequence of uncoupled optimality systems of local-in-time optimal control problems. In the limit full recovery of the coupling conditions is achieved, and, hence, the local solutions and controls converge to the global ones. The process is inherently parallel and is suitable for real-time control applications.}, author = {Langnese, John E. and Leugering, Günter}, doi = {10.1051/cocv:2002042}, faupublication = {no}, journal = {Esaim-Control Optimisation and Calculus of Variations}, keywords = {Maxwell system;optimal control;domain decomposition; 65N55; 49M27; 35Q60}, pages = {775-799}, peerreviewed = {Yes}, title = {{Time} domain decomposition in final value optimal control of the {Maxwell} system}, url = {http://www.esaim-cocv.org/articles/cocv/abs/2002/02/Lagnese/Lagnese.html}, volume = {8}, year = {2002} } @article{faucris.121753104, abstract = {We study optimal control problems for linear systems with prescribed initial and terminal states. We analyze the exact penalization of the terminal constraints. We show that for systems that are exactly controllable, the norm-minimal exact control can be computed as the solution of an optimization problem without terminal constraint but with a nonsmooth penalization of the end conditions in the objective function, if the penalty parameter is sufficiently large. We describe the application of the method for hyperbolic and parabolic systems of partial differential equations, considering the wave and heat equations as particular examples. Copyright © 2016 John Wiley & Sons, Ltd.}, author = {Gugat, Martin and ZuaZua, Enrique}, doi = {10.1002/oca.2238}, faupublication = {yes}, journal = {Optimal Control Applications & Methods}, keywords = {exact controllability;optimal control;terminal constraint;exact penalization;wave equation;heat equation;moment equations;method of moments;L1 optimal control;abstract Cauchy problems;nonsmooth optimization}, peerreviewed = {Yes}, title = {{Exact} penalization of terminal constraints for optimal control problems}, url = {http://onlinelibrary.wiley.com/doi/10.1002/oca.2238/abstract}, volume = {37}, year = {2016} } @article{faucris.107398324, abstract = {In this contribution the optimal boundary control problem for a first order nonlinear, nonlocal hyperbolic PDE is studied. Motivated by various applications ranging from re-entrant manufacturing systems to particle synthesis processes, we establish the regularity of solutions for W1,p-data. Based on a general L2 tracking type cost functional, the existence, uniqueness, and regularity of the adjoint system in W1,p is derived using the special structure induced from the nonlocal flux function of the state equation. The assumption of W1,p - and not Lp-regularity comes thereby due to the fact that the adjoint equation asks for more regularity to be well defined. This problem is discussed in detail, and we give a solution by defining a special type of cost functional, such that the corresponding optimality system is well defined.}, author = {Gröschel, Michael and Keimer, Alexander and Leugering, Günter and Wang, Zhiqiang}, doi = {10.1137/120873832}, faupublication = {yes}, journal = {SIAM Journal on Control and Optimization}, pages = {2141--2163}, peerreviewed = {Yes}, title = {{Regularity} {Theory} and {Adjoint}-{Based} {Optimality} {Conditions} for a {Nonlinear} {Transport} {Equation} with {Nonlocal} {Velocity}}, volume = {52}, year = {2014} } @article{faucris.122686784, abstract = {A problem of image registration is considered in the context of optimal mass transportation. The properties and limitations of an optimal image transportation are analyzed. A modified formulation of this approach is proposed in order to overcome the morphing effect. Finally, a fast and simple scale-space approach for the new formulation is introduced, and numerical examples are presented.}, author = {Museyko, Oleg and Stiglmayr, Michael and Klamroth, Kathrin and Leugering, Günter}, doi = {10.1137/080721522}, faupublication = {yes}, journal = {Siam Journal on Imaging Sciences}, keywords = {image registration;image morphing;optimal mass transportation;Monge-Kantorovich problem; 94A08; 92C55; 49N99}, month = {Jan}, pages = {1068-1097}, peerreviewed = {Yes}, title = {{On} the {Application} of the {Monge}-{Kantorovich} {Problem} to {Image} {Registration}}, url = {http://epubs.siam.org/doi/abs/10.1137/080721522?journalCode=sjisbi}, volume = {2}, year = {2009} } @incollection{faucris.117650104, abstract = {We consider shape optimization for objects illuminated by light. More precisely, we focus on time-harmonic solutions of the Maxwell system in}, author = {Semmler, Johannes and Bley, Karina and Klupp Taylor, Robin and Stingl, Michael and Vogel, Nicolas}, doi = {10.1002/adfm.201806025}, faupublication = {yes}, journal = {Advanced Functional Materials}, peerreviewed = {unknown}, title = {{Particulate} {Coatings} with {Optimized} {Haze} {Properties}}, url = {https://onlinelibrary.wiley.com/doi/full/10.1002/adfm.201806025}, volume = {5}, year = {2018} } @incollection{faucris.122069024, address = {Oberwolfach}, author = {Leugering, Günter and Kocvara, Michal and Stingl, Michael}, booktitle = {Optimal Control of Coupled Systems of PDE}, doi = {10.4171/OWR/2008/13}, editor = {Karl Kunisch, Günter Leugering, Jürgen Sprekels and Fredi Tröltzsch}, faupublication = {yes}, pages = {647-649}, peerreviewed = {unknown}, publisher = {European Mathematical Society Publishing House}, series = {Oberwolfach Reports}, title = {{A} {New} {Method} for the {Solution} of {Multi}-{Disciplinary} {Free} {Material} {Optimization} {Problems}}, volume = {13}, year = {2008} } @article{faucris.107383364, abstract = {The aim of our work is to develop optimal dielectric composite structures with specific qualities. The task is to design interfaces of given material components such that the originated structure attains certain optical properties. Propagation of the electromagnetic waves in the composite is described by the Helmholtz equation. Success of the structure is enumerated by the objective function which is to be minimized. Interfaces of the given materials are parametrized by the cubic B–spline curves. The design variables are afterwards the positions of B–spline control points. For objective function evaluation one forward computation of the Helmholtz equation is needed. To get the sensitivity of the objective function we solve the backward (adjoint) equation.}, author = {Seifrt, Frantiek and Leugering, Günter and Rohan, Eduard}, doi = {10.1002/pamm.200810705}, faupublication = {yes}, journal = {Proceedings in Applied Mathematics and Mechanics}, pages = {10705-10706}, peerreviewed = {Yes}, title = {{Shape} optimization for the {Helmholtz} equation}, url = {http://onlinelibrary.wiley.com/doi/10.1002/pamm.200810705/full}, volume = {8}, year = {2008} } @article{faucris.217149148, abstract = {For most particle-based applications, formulation in the liquid phase is a decisive step, and thus, particle interactions and stability in liquid media are of major importance. The concept of Hansen solubility parameters (HSP) was initially invented to describe the interactions of (polymer) molecules and their solubility in different liquids and is increasingly being used in particle technology to describe dispersibility. Because dispersions are not thermodynamically stable, the term Hansen dispersibility parameters (HDP) is used instead of HSP (Süß, Sobisch, Peukert, Lerche, & Segets, 2018). Herein, we extend a previously developed standardized and non-subjective method for determination of Hansen parameters based on analytical centrifugation to the important class of quantum materials. As a technically relevant model system, zinc oxide quantum dots (QDs) were used to transfer our methodology to nanoparticles (NPs) with sizes below 10 nm. The results obtained using the standard procedure starting from a dried powder were compared with those obtained through redispersion from the wet sediment produced during the typical washing procedure of QDs, and drying was observed to play an important role. In conclusion, our study reveals the high potential of HDP for quantifying the interfacial properties of NPs as well as their link to dispersibility.}, author = {Süß, Sebastian and Lin, Wei and Getmanenko, Olga and Pflug, Lukas and Sobisch, Titus and Peukert, Wolfgang and Lerche, Dietmar and Segets, Doris}, doi = {10.1016/j.partic.2018.05.010}, faupublication = {yes}, journal = {Particuology}, keywords = {Colloidal stability; Functionalization; Hansen solubility parameter; Quantum material; Semiconductor nanoparticles}, note = {CRIS-Team Scopus Importer:2019-05-09}, pages = {71-79}, peerreviewed = {Yes}, title = {{Suspension}- and powder-based derivation of {Hansen} dispersibility parameters for zinc oxide quantum dots}, volume = {44}, year = {2019} } @phdthesis{faucris.123772044, author = {Hante, Falk}, faupublication = {yes}, peerreviewed = {automatic}, school = {Friedrich-Alexander-Universität Erlangen-Nürnberg}, title = {{Hybrid} {Dynamics} {Comprising} {Modes} {Governed} by {Partial} {Differential} {Equations}: {Modeling}, {Analysis} and {Control} for {Semilinear} {Hyperbolic} {Systems} in {One} {Space} {Dimension}}, url = {http://nbn-resolving.de/urn/resolver.pl?urn=urn:nbn:de:bvb:29-opus-19356}, year = {2010} } @article{faucris.217952993, abstract = {In this paper, we study a nonlinear Caputo fractional boundary value problem on a star graph. By means of transformation, an equivalent system of fractional boundary value problem is obtained. Then we establish the existence and uniqueness results by fixed point theory: in particular, using Banach's contraction principle and Schaefer's fixed point theorem. We also present some examples to illustrate the application of our results.}, author = {Mehandiratta, Vaibhav and Mehra, Mani and Leugering, Günter}, doi = {10.1016/j.jmaa.2019.05.011}, faupublication = {yes}, journal = {Journal of Mathematical Analysis and Applications}, keywords = {Boundary value problem; Caputo fractional derivative; Differential equation on graphs; Fixed point theorems}, note = {CRIS-Team Scopus Importer:2019-05-21}, peerreviewed = {Yes}, title = {{Existence} and uniqueness results for a nonlinear {Caputo} fractional boundary value problem on a star graph}, year = {2019} } @article{faucris.123696804, abstract = {We study a Dirichlet optimal control problem for a quasi-linear monotone elliptic equation, the so-called weighted p-Laplacian problem. The coefficient of the -Laplacian, the weight u, we take as a control in BV (Ω) ∩ L∞(Ω). In this article, we use box-type constraints for the control such that there is a strictly positive lower and some upper bound. In order to handle the inherent degeneracy of the -Laplacian, we use a regularization, sometimes referred to as the -Laplacian. We derive existence and uniqueness of solutions to the underlying boundary value problem and the optimal control problem. In fact, we introduce a two-parameter model for the weighted -Laplacian, where we approximate the nonlinearity by a bounded monotone function, parametrized by κ. Further, we discuss the asymptotic behavior of the solutions to the regularized problem on each (ϵ, κ)-level as the parameters tend to zero and infinity, respectively.}, author = {Casas, Eduardo and Kogut, Peter I. and Leugering, Günter}, doi = {10.1137/15M1028108}, faupublication = {yes}, journal = {SIAM Journal on Control and Optimization}, keywords = {Control in coefficients; Nonlinear Dirichlet problem; Optimal control}, pages = {1406-1422}, peerreviewed = {Yes}, title = {{Approximation} of optimal control problems in the coefficient for the p-{Laplace} equation. {I}. {Convergence} result}, volume = {54}, year = {2016} } @article{faucris.111889844, abstract = {We consider a finite string that is fixed at one end and subject to a feedback control at the other end which is allowed to move. We show that the behaviour is similar to the situation where both ends are fixed: As long as the movement is not too fast, the energy decays exponentially and for a certain parameter in the feedback law it vanishes in finite time. We consider movements of the boundary that are continuously differentiable with a derivative whose absolute value is smaller than the wave speed. We solve a problem of worst-case optimal feedback control, where the parameter in the feedback law is chosen such that the worst-case L p -norm of the space derivative at the fixed end of the string is minimized (p ∈ 1, ∞)). We consider the worst case both with respect to the initial conditions and with respect to the boundary movement. It turns out that the parameter for which the energy vanishes in finite time is optimal in this sense for all p. © The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.}, author = {Gugat, Martin}, doi = {10.1093/imamci/dnm014}, faupublication = {yes}, journal = {IMA Journal of Mathematical Control and Information}, keywords = {Feedback; Moving boundary; Optimal boundary control; Optimal control of PDEs; PDE constrained optimization; Wave equation}, note = {UnivIS-Import:2015-03-09:Pub.2008.nat.dma.zentr.optima_5}, pages = {111-121}, peerreviewed = {Yes}, title = {{Optimal} boundary feedback stabilization of a string with moving boundary}, url = {http://imamci.oxfordjournals.org/cgi/content/abstract/dnm014?ijkey=sCu0noGNy5dtzdd&keytype=ref}, volume = {25}, year = {2008} } @article{faucris.106688824, author = {Rüffler, Fabian and Hante, Falk}, doi = {10.1016/j.nahs.2016.05.001}, faupublication = {yes}, journal = {Nonlinear Analysis: Hybrid Systems}, keywords = {Partial differential equation }, pages = {215 - 227}, peerreviewed = {unknown}, title = {{Optimal} switching for hybrid semilinear evolutions}, url = {http://www.sciencedirect.com/science/article/pii/S1751570X16300231}, volume = {22}, year = {2016} } @article{faucris.111889624, abstract = {In many control application, switching between different control devices occurs. Here the problem to control a finite string to the zero state in finite time by controlling the state at the two boundary points is considered, where at each moment in time one of the boundary controls must be switched off, that is its control value must be equal to zero. The corresponding optimal control problem where the objective function is the L

A vibrating plate is here taken to satisfy the model equation:*u*_{tt} + Δ^{2}u = 0 (where*Δ*^{2}u:= Δ(Δu); Δ = Laplacian) with boundary conditions of the form:*u*_{v} = 0 and*(Δu)*_{v} = ϕ = control. Thus, the state is the pair [*u, u*_{t}] and controllability means existence of*ϕ* on Σ:= (0,*T*)×*∂Ω* transfering ‘any’*[u, u*_{t}]_{0} to ‘any’*[u, u*_{t}]_{T}. The formulation is given by eigenfunction expansion and duality. The substantive results apply to a rectangular plate. For large*T* one has such controllability with*∥ϕ∥ = O(T*^{−1/2}). More surprising is that (based on a harmonic analysis estimate [11]) one has controllability for arbitrarily short times (in contrast to the wave equation:*u*_{tt} = Δu) with log*∥ϕ∥ = O(T*^{−1}) as*T*→0. Some related results on minimum time control are also included.

}, author = {Leugering, Günter and Krabs, W. and Seidman, Thomas I.}, doi = {10.1007/BF01442208}, faupublication = {no}, journal = {Applied Mathematics and Optimization}, pages = {205-229}, peerreviewed = {Yes}, title = {{ON} {BOUNDARY} {CONTROLLABILITY} {OF} {A} {VIBRATING} {PLATE}}, url = {http://link.springer.com/article/10.1007/BF01442208}, volume = {13}, year = {1985} } @book{faucris.108768264, address = {Berlin}, author = {Jahn, Johannes}, edition = {3}, faupublication = {yes}, note = {UnivIS-Import:2015-04-02:Pub.1994.nat.dma.pama21.introd}, pages = {249}, publisher = {Springer}, title = {{Introduction} to the {Theory} of {Nonlinear} {Optimization}}, year = {2007} } @article{faucris.119402844, abstract = {The feasible set of a convex semi-infinite program is described by a possibly infinite system of convex inequality constraints. We want to obtain an upper bound for the distance of a given point from this set in terms of a constant multiplied by the value of the maximally violated constraint function in this point. Apart from this Lipschitz case we also consider error bounds of Hölder type, where the value of the residual of the constraints is raised to a certain power. We give sufficient conditions for the validity of such bounds. Our conditions do not require that the Slater condition is valid. For the definition of our conditions, we consider the projections on enlarged sets corresponding to relaxed constraints. We present a condition in terms of projection multipliers, a condition in terms of Slater points and a condition in tenus of descent directions. For the Lipschitz case, we give five equivalent characterizations of the validity of a global error bound. We extend previous results in two directions: First, we consider infinite systems of inequalities instead of finite systems. The second point is that we do not assume that the Slater condition holds which has been required in almost all earlier papers. © Springer-Verlag 2000.}, author = {Gugat, Martin}, doi = {10.1007/s101070050016}, faupublication = {no}, journal = {Mathematical Programming}, keywords = {Convex inequalities; Dual solutions; Error bounds; Hölder error bound; Mangasarian-Fromovitz condition; Projection multipliers; Semi-infinite program; Weak slater condition; 20E28; 20G40; 20C20}, note = {UnivIS-Import:2015-03-09:Pub.2000.nat.dma.lama1.errorb}, pages = {255-275}, peerreviewed = {Yes}, title = {{Error} bounds for infinite systems of convex inequalities without {Slater}'s condition}, url = {http://www.springerlink.com/app/home/contribution.asp?wasp=f62clce4kc2rww8fa45u&referrer=parent&backto=issue,3,10;journal,31,44;linkingpublicationresults,id:103081,1}, volume = {88}, year = {2000} } @article{faucris.122687444, abstract = {We consider a star-graph as an examplary network, with elastic strings stretched along the edges. The network is allowed to perform out-of-the plane displacements. We consider such networks as being controlled at its simple nodes via Dirichlet conditions. The objective is to steer given initial data to final target data in a given time T with minimal control costs. This problem is discussed in the continuous as well as in the discrete case. We discuss an iterative domain decomposition technique and its discrete analogue. We prove convergence and show some numerical results. (C) 2000 Elsevier Science B.V. All rights reserved.}, author = {Leugering, Günter}, doi = {10.1016/S0377-0427(00)00307-1}, faupublication = {no}, journal = {Journal of Computational and Applied Mathematics}, keywords = {domain decomposition;networks of strings;optimal control;semi-discrete models}, pages = {133-157}, peerreviewed = {Yes}, title = {{On} the semi-discretization of optimal control problems for networks of elastic strings: global optimality systems and domain decomposition}, url = {http://www.sciencedirect.com/science/article/pii/S0377042700003071}, volume = {120}, year = {2000} } @inproceedings{faucris.214864375, abstract = {In e-Learning environments, the Learning Management Systems (LMS) play a central role.

The LMS Moodle and ILIAS are widely used at universities and Universities of Applied

Sciences. But even nowadays, it is still a challenge to use the possibilities given by digital

materials to create learning content which offers more than a classical textbook. Several

tools are available to show, explain and dynamically explore mathematical concepts,

among them are CoCalc (former SageMathCloud), SageCell, CDF-Player, JSXGraph and

GeoGebra. It is still quite common that content for a lecture is provided inside the local

LMS, while the learner has to open another platform or software to use the dynamic

mathematical tools for exploration of the content. In our contribution (talk or poster) we

will show our approaches to include dynamic mathematics inside LMS.

In particular, we use JSXGraph for dynamic 2D diagrams and the SageMathCell for a wide

range of mathematical aspects. JSXGraph is a JavaScript library, which is quite easy to use

and which offers the possibility to include user interactions via HTML-forms. The

advantage is that the computations are done in the browser on client-side. On the other

hand, SageMathCell has a huge variety of tools already included, like Maxima, R, Octave

or Python. Furthermore, it is very easy to show 3D-diagrams. This is made possible by

executing the computation on a remote server, which has to be connected from the content.

We include JSXGraph and SageMathCell in classical HTML-Pages as media content and

through dedicated plug-ins for the LMS Moodle and ILIAS. During the ”Mathematics for

Engineers” (part 1-3) we provide additional material for several topics, e.g. series, (un)-

constrained optimization, integration, parametrization of curves and surfaces or differential

equations. We see the advantage that the diagrams will become an integral part of the

learning modules and the learning unit does not look like patchwork.

Further, the learners can focus on the content and do not have to bring additional software

or to login in a second learning platform. During presence lectures the lecturer can use the

same LMS as the learnersdo for their follow-up work.

For JSXGraph, there is a plug-in for Moodle, for the usage of SageMathCell inside ILIAS

the first author could initiate the development.

Elliptic control by penalty techniques with control reduction, in

2-regularity for the initial position and H

The number of dual-career couples with children is growing fast. These

couples face various challenging problems of organizing their lifes, in par-

ticular connected with childcare and time-management. As a typical ex-

ample we study one of the difficult decision problems of a dual career

couple from the point of view of operations research with a particular

focus on gender equality, namely the location problem to find a family

home. This leads to techniques that allow to include the value of gender

equality in rational decision processes.

},
author = {Gugat, Martin and Abele-Brehm, Andrea and Klamroth, Kathrin},
faupublication = {yes},
keywords = {Dual Careec couples, Optimal Location Problem, Childcare Management},
peerreviewed = {automatic},
title = {{Optimal} location of family homes for dual career couples},
url = {http://www.optimization-online.org/DB_HTML/2010/02/2547.html},
year = {2010}
}
@article{faucris.220859888,
abstract = {We consider nonlinear and nonsmooth mixing aspects in gas transport optimization problems. As mixed-integer reformulations of pooling-type mixing models already render small-size instances computationally intractable, we investigate the applicability of smooth nonlinear programming techniques for equivalent complementarity-based reformulations. Based on recent results for remodeling piecewise affine constraints using an inverse parametric quadratic programming approach, we show that classical stationarity concepts are meaningful for the resulting complementarity-based reformulation of the mixing equations. Further, we investigate in a numerical study the performance of this reformulation compared to a more compact complementarity-based one that does not feature such beneficial regularity properties. All computations are performed on publicly available data of real-world size problem instances from steady-state gas transport.},
author = {Hante, Falk and Schmidt, Martin},
doi = {10.1007/s13675-019-00112-w},
faupublication = {yes},
journal = {EURO Journal on Computational Optimization},
keywords = {Complementarity constraints; Gas transport networks; Inverse parametric quadratic programming; Mixing; MPCC},
note = {CRIS-Team Scopus Importer:2019-06-18},
peerreviewed = {Yes},
title = {{Complementarity}-based nonlinear programming techniques for optimal mixing in gas networks},
year = {2019}
}
@article{faucris.121714164,
abstract = {Resonance frequency analysis (RFA) using the Osstell device (Osstell AB, Gothenburg, Sweden) has been advocated for quantifying implant stability on a relative scale of implant stability quotients (ISQ). It was the goal of this prospective clinical study to evaluate whether a certain ISQ level, at the time an implant is placed, correlates with successful osseointegration as some have claimed. Four hundred ninety-five implants (Straumann AG, Basel, Switzerland), varying in length and diameter, were placed in a private practice, strictly adhering to the implant manufacturer's surgical protocol. After placement and after healing periods of 42 days in the mandible and 56 days (implant manufacturer's protocol) in the maxilla, implant stability was measured using RFA. After healing, implants were torqued forward at 35 Ncm and allowed to heal further if the patients felt discomfort. Statistical analysis of the data obtained was based on Welch tests and Kolmogorov-Smirnow tests (level of significance ? = 0.05). Results showed that 432 implants were osseointegrated after the predefined healing periods while 8 implants were lost and, in 55 cases, healing was prolonged. Both at insertion (P = .025) and after healing (P < .001), successful implants showed significantly different ISQ values as compared to implant failures or implants with prolonged healing. However, overlapping ISQ distributions at implant insertion demonstrated that there was no correlation among the data that could be used to predict successful osseointegration. Within the limits of this study, the prognostic value of ISQ values appears to be ambiguous.},
author = {Krafft, Tim and Graef, Friedrich and Karl, Matthias},
doi = {10.1563/AAID-JOI-D-13-00172},
faupublication = {yes},
journal = {The Journal of oral implantology},
note = {EVALuna2:24823},
pages = {e133-7},
peerreviewed = {Yes},
title = {{Osstell} {Resonance} {Frequency} {Measurement} {Values} as a {Prognostic} {Factor} in {Implant} {Dentistry}},
volume = {41},
year = {2015}
}
@incollection{faucris.116884504,
abstract = {We consider a network where a dynamical process governed by hyperbolic conservation laws takes place. At the vertices, the conservation laws are coupled by algebraic node conditions. The system is also controlled at the vertices through these conditions. To solve problems of optimal control for such a system, an adjoint sensitivity calculus is useful since it allows the efficient evaluation of the gradient of the objective function. We present such a calculus in the framework of classical solutions.},
address = {Boca Raton},
author = {Gugat, Martin},
booktitle = {Control and Boundary Analysis},
editor = {John Cagnol and Jean-Paul Zolesio},
faupublication = {yes},
keywords = {Sensitivy calculus, adkoint system},
note = {UnivIS-Import:2015-04-20:Pub.2005.nat.dma.lama1.nodalc},
pages = {201-214},
peerreviewed = {Yes},
publisher = {Chapman & Hall/CRC Press},
series = {Pure and Applied Mathematics},
title = {{Nodal} {Control} of {Conservation} {Laws} on {Networks}},
volume = {240},
year = {2005}
}
@incollection{faucris.118332544,
address = {München},
author = {Jahn, Johannes},
booktitle = {Ausgewählte Operations Research Software in FORTRAN},
editor = {H. Späth},
faupublication = {no},
note = {UnivIS-Import:2015-04-17:Pub.1979.nat.dma.pama21.lsungn},
pages = {30-50},
peerreviewed = {unknown},
publisher = {Oldenbourg},
title = {{Lösung} nichtlinearer {Optimierungsprobleme} mit {Nebenbedingungen}},
year = {1979}
}
@article{faucris.122291224,
abstract = {We consider a thin elastic plate with piezo patches mounted on top of it. Electrodes are located on the upper and, depending on the devices, at the lower surface of the patches. This piezo actuator is coupled to an elastic body. We develop an asymptotic procedure to derive a two-dimensional approximation of the entire structure. As a result, we obtain an inhomogeneous fourth-order plate equation with piecewise smooth coefficients for the vertical displacement coupled to a second-order in-plane problem. The analysis and the resulting asymptotic limits help clarifying the modeling issue concerning active piezo devices in multidimensional smart structures. Copyright © 2012 John Wiley & Sons, Ltd.},
author = {Leugering, Günter and Nazarov, Serguei A. and Slutskij, Andrey S.},
doi = {10.1002/mma.1566},
faupublication = {yes},
journal = {Mathematical Methods in the Applied Sciences},
keywords = {anisotropic material; Asymptotic analysis; effective material; piezoelectric material; plate equation},
pages = {633-658},
peerreviewed = {Yes},
title = {{Asymptotic} analysis of {3D} thin anisotropic plates with a piezoelectric patch},
volume = {35},
year = {2012}
}
@incollection{faucris.121892804,
abstract = {Many important topics in multiobjective optimization and decision making have been studied in this book so far. In this chapter, we wish to discuss some new trends and challenges which the field is facing. For brevity, we here concentrate on three main issues: new problem areas in which multiobjective optimization can be of use, new procedures and algorithms to make efficient and useful applications of multiobjective optimization tools and, finally, new interesting and practically usable optimality concepts. Some research has already been started and some such topics are also mentioned here to encourage further research. Some other topics are just ideas and deserve further attention in the near future. © 2008 Springer Berlin Heidelberg.},
address = {Berlin},
author = {Jahn, Johannes and Miettinen, K. and Ogryczak, W. and Deb, K. and Shimoyama, K. and Vetschera, R.},
booktitle = {Multiobjective Optimization - Interactive and Evolutionary Approaches},
doi = {10.1007/978-3-540-88908-3-16},
editor = {J. Branke, K. Deb, K. Miettinen, R. Slowinski},
faupublication = {yes},
isbn = {3540889078},
note = {UnivIS-Import:2015-04-20:Pub.2008.nat.dma.pama21.future},
pages = {435-461},
peerreviewed = {unknown},
publisher = {Springer-verlag},
series = {Lecture Notes in Computer Science},
title = {{Future} {Challenges}},
volume = {5252 LNCS},
year = {2008}
}
@article{faucris.123262964,
abstract = {While the numerical discretization of one-dimensional blood flow models for vessels with viscoelastic wall properties is widely established, there is still no clear approach on how to couple one-dimensional segments that compose a network of viscoelastic vessels. In particular for Voigt-type viscoelastic models, assumptions with regard to boundary conditions have to be made, which normally result in neglecting the viscoelastic effect at the edge of vessels. Here we propose a coupling strategy that takes advantage of a hyperbolic reformulation of the original model and the inherent information of the resulting system. We show that applying proper coupling conditions is fundamental for preserving the physical coherence and numerical accuracy of the solution in both academic and physiologically relevant cases. (C) 2016 Elsevier Inc. All rights reserved.},
author = {Müller, Lukas and Leugering, Günter and Blanco, Pablo J.},
doi = {10.1016/j.jcp.2016.03.012},
faupublication = {yes},
journal = {Journal of Computational Physics},
keywords = {Finite volume schemes;Viscoelasticity;Junctions;One-dimensional blood flow},
pages = {167-193},
peerreviewed = {Yes},
title = {{Consistent} treatment of viscoelastic effects at junctions in one-dimensional blood flow models},
url = {http://www.sciencedirect.com/science/article/pii/S0021999116001649},
volume = {314},
year = {2016}
}
@inproceedings{faucris.114001184,
author = {Rathmann, Wigand},
booktitle = {4. SAXON SIMULATION MEETING and Mathcad-Workshop},
date = {2012-04-16/2012-04-17},
faupublication = {yes},
peerreviewed = {No},
publisher = {TU Chemnitz, Professur für Montage- und Handhabungstechnik},
title = {{Parameterschätzung} in gewöhnlichen {Differentialgleichungen}},
url = {http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-84901},
year = {2012}
}
@article{faucris.117637344,
abstract = {A new method for the optimal design of inhomogeneous meso-structured components is presented. The method is based on a variant of the free material optimization (FMO) method. Instead of coupling a macroscopic model directly with the meso-scale in the framework of a two-scale approach, information from the meso-scale is incorporated into the FMO model by additional constraints. The FMO result, given in terms of optimized tensors, is interpreted by the inverse homogenization approach. Rather than only computing the meso-structure for each "FMO cell" independently, approximate continuity of the meso-structure is enforced. Thus, the final result is a manufacturable structurally graded material. The feasibility of the whole method is demonstrated by means of an academic example.},
author = {Schury, Fabian and Stingl, Michael and Wein, Fabian},
doi = {10.1137/110850335},
faupublication = {yes},
journal = {SIAM Journal on Scientific Computing},
keywords = {free material optimization;inverse homogenization;structurally graded materials;topology optimization;numerical validation},
month = {Jan},
pages = {B711-B733},
peerreviewed = {Yes},
title = {{Efficient} two-scale optimization of manufacturable graded structures},
volume = {34},
year = {2012}
}
@incollection{faucris.120448064,
author = {Jahn, Johannes},
booktitle = {Methods of Operations Research},
faupublication = {yes},
note = {UnivIS-Import:2015-03-05:Pub.1987.nat.dma.pama21.proble},
pages = {51-59},
peerreviewed = {unknown},
title = {{Problems} of {Vector} {Optimization}},
volume = {57},
year = {1987}
}
@article{faucris.120457084,
author = {Jahn, Johannes and Luc, D.T.},
faupublication = {yes},
journal = {Numerical Functional Analysis and Optimization},
note = {UnivIS-Import:2015-03-05:Pub.1992.nat.dma.pama21.axioma},
pages = {305-326},
peerreviewed = {Yes},
title = {{Axiomatic} {Approach} to {Duality} in {Optimization}},
volume = {13},
year = {1992}
}
@incollection{faucris.117664184,
abstract = {The optimal design and control of infrastructures, e.g. in traffic control, water-supply, sewer-systems and gas-pipelines, the optimization of structures, form and formation of materials, e.g. in lightweight structures, play a predominant role in modern fundamental and applied research. However, until very recently, simulation-based optimization has been employed in the sense that parameters are being adjusted in a forward simulation using either ‘trial-and-error’ or a few steps of a rudimentary unconstrained derivative-free and mostly stochastic optimization code. It has become clear by now that instead often a model-based and more systematic constrained optimization that exploits the structure of the problem under consideration may outperform the former more naive approaches. Thus, modern mathematical optimization methods respecting constraints in state and design variables can be seen as a catalyst for recent and future technologies. More and more success stories can be detected in the literature and even in the public press which underline the role of optimization as a key future technology. In particular, optimization with partial differential equations (PDEs) as constraints, or in other words ‘PDE-constrained optimization’ has become research topic of great influence. A DFG-Priority-Program (PP) has been established by the German Science Foundation (DFG) in 2006 in which well over 25 project are funded throughout Germany. The PP focuses on the interlocking of fundamental research in optimization, modern adaptive, hierarchical and structure exploiting algorithms, as well as visualization and validation. With similar goals in mind, a European network within the European Science Foundation (ESF) ‘PDE-constrained Optimization’ has been recently established that provides a European platform for this cutting edge technology. In this report the authors dwell on exemplary areas of their expertise within applications that are already important and will increasingly dominate future developments in mechanical and civil engineering. These applications are concerned with optimal material and design in material sciences and light-weight structures as well as real-time capable optimal control of flows in transportation systems such as gas-pipeline networks. ‘Advanced Materials’, ‘Energy-Efficiency’ and ‘Transport’ are key problems for the future society which definitely deserve public funding by national and international agencies.},
address = {Berlin Heidelberg},
author = {Leugering, Günter and Martin, Alexander and Stingl, Michael},
booktitle = {Production Factor Mathematics},
doi = {10.1007/978-3-642-11248-5_14},
editor = {Martin Grötschel, Klaus Lucas, Volker Mehrmann},
faupublication = {yes},
pages = {263-276},
peerreviewed = {unknown},
publisher = {Springer},
title = {{Topology} and {Dynamic} {Networks}: {Optimization} with {Application} in {Future} {Technologies}},
year = {2010}
}
@article{faucris.113416204,
abstract = {
We consider refinement of finite element discretizations by splitting nodes along edges. For

this process, we derive asymptotic expansions of Galerkin solutions of linear second-order

elliptic equations. Thereby, we calculate a topological derivative w.r.t. node insertion for

functionals such as the total potential energy, minimization of which decreases the approxi-

mation error in the energy norm. Hence, these sensitivities can be used to define indicators for

local h-refinement. Our results suggest that this procedure leads to an efficient adaptive re-

finement method. This presentation is concerned with a model problem in 1d. The extension

of this concept to higher dimensions will be the subject of forthcoming publications.

},
author = {Friederich, Jan and Leugering, Günter and Steinmann, Paul},
doi = {10.1002/gamm.201210012},
faupublication = {yes},
journal = {GAMM-Mitteilungen},
note = {UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.anadap},
pages = {175-190},
peerreviewed = {unknown},
title = {{An} adaptive finite element method based on sensitivities for node insertion},
url = {http://onlinelibrary.wiley.com/doi/10.1002/gamm.201210012/full},
volume = {35},
year = {2012}
}
@article{faucris.111078044,
abstract = {We consider the problem of boundary optimal control of a wave equation with boundary dissipation by the way of time-domain decomposition of the corresponding optimality system. We develop an iterative algorithm which shows that the decomposed optimality system corresponds to local-in-time optimal control problems which can be treated in parallel. We show convergence of the algorithm. Finally, we provide a time discretization which is reminiscent of an instantaneous control scheme. We thereby also contribute to the problem of convergence of such schemes. (C) 2002 Elsevier Science B.V. All rights reserved.},
author = {Langnese, John E. and Leugering, Günter},
doi = {10.1016/S0167-6911(02)00268-2},
faupublication = {no},
journal = {Systems & Control Letters},
keywords = {time-domain decomposition;optimality systems;instantaneous control},
pages = {229-242},
peerreviewed = {Yes},
title = {{Time}-domain decomposition of optimal control problems for the wave equation},
url = {http://www.sciencedirect.com/science/article/pii/S0167691102002682},
volume = {48},
year = {2003}
}
@incollection{faucris.118333644,
address = {Berlin},
author = {Jahn, Johannes},
booktitle = {Operations Research Proceedings 1987},
editor = {H. Schellhaas, P. van Beek, H. Isermann, R. Schmidt, M. Zijlstra},
faupublication = {yes},
note = {UnivIS-Import:2015-04-17:Pub.1988.nat.dma.pama21.ametho},
pages = {576-587},
peerreviewed = {unknown},
publisher = {Springer},
title = {{A} {Method} of {Reference} {Point} {Approximation} in {Vector} {Optimization}},
year = {1988}
}
@article{faucris.202369309,
author = {Keimer, Alexander and Pflug, Lukas and Spinola, Michele},
doi = {10.1016/j.jmaa.2018.05.013},
faupublication = {yes},
journal = {Journal of Mathematical Analysis and Applications},
keywords = {Method of characteristics; Fixed-point problem; Nonlocal conservation law; Multi-dimensional nonlocal balance law; Well-posedness; Regularity},
pages = {18-55},
peerreviewed = {Yes},
title = {{Existence}, uniqueness and regularity of multi-dimensional nonlocal balance laws with damping},
volume = {466},
year = {2018}
}
@article{faucris.117907504,
abstract = {We consider an elliptic distributed quadratic optimal control problem with exact controllability constraints on a part of the domain which, in turn, is parametrized by a small parameter e. The quadratic tracking type functional is defined on the remaining part of the domain. We thus consider a family of optimal control problems with state equality constraints. The purpose of this paper is to study the asymptotic limit of the optimal control problems as the parameter e tends to zero. The analysis presented is in the spirit of the direct approach of the calculus of variations. This is achieved in the framework of relaxed problems. We finally apply the procedure to an optimal control problem on a perforated domain with holes of critical size. It is shown that a strange term in the terminology of Cioranescu and Murat (Prog. Nonlinear Diff. Eq. Appl., Vol. 31, Birkhauser-Verlag, Boston, 1997, pp. 49-93) appears in the limiting homogenized problem.},
author = {Kogut, Peter I. and Leugering, Günter},
doi = {10.3233/ASY-2008-0871},
faupublication = {yes},
journal = {Asymptotic Analysis},
keywords = {controllability constraints;relaxed problems;gamma(Delta) and Gamma-convergence;perforated domains},
month = {Jan},
pages = {229-249},
peerreviewed = {Yes},
title = {{Homogenization} of {Dirichlet} optimal control problems with exact partial controllability constraints},
url = {http://content.iospress.com/articles/asymptotic-analysis/asy871},
volume = {57},
year = {2008}
}
@article{faucris.110506044,
author = {Mitschke, Holger and Schwerdtfeger, Jan and Schury, Fabian and Stingl, Michael and Körner, Carolin and Singer, Robert and Robins, Vanessa and Mecke, Klaus and Schröder-Turk, Gerd},
doi = {10.1002/adma.201190118},
faupublication = {yes},
journal = {Advanced Materials},
pages = {2669-2674},
peerreviewed = {Yes},
title = {{Erratum}: {Finding} auxetic frameworks in periodic tessellations},
volume = {23},
year = {2011}
}
@masterthesis{faucris.118445184,
abstract = {In der vorliegenden Arbeit werden zwei numerische Verfahren für die Registrierung medizinischer Bilddaten vorgestellt. Beide Verfahren beruhen auf der numerischen Lösung eines Optimierungsproblems, welches eine Transportgleichung als Nebenbedingung besitzt. Der Lösungsalgorithmus koppelt ein Innere-Punkte-Verfahren für das Optimierungsproblem mit einem Finite-Elemente-Verfahren für die Transportgleichung.},
author = {Hild, Johannes},
faupublication = {yes},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Numerische} {Verfahren} für optimalen {Massentransport} in der {Registrierung} medizinischer {Bilddaten}},
year = {2007}
}
@inproceedings{faucris.117639104,
abstract = {In this article, we present the Free Material Optimization (FMO) problem for plates and shells based on Naghdi's shell model. In FMO - a branch of structural optimization - we search for the ultimately best material properties in a given design domain loaded by a set of given forces. The optimization variable is the full material tensor at each point of the design domain. We give a basic formulation of the problem and prove existence of an optimal solution. Lagrange duality theory allows to identify the basic problem as the dual of an infinite-dimensional convex nonlinear semidefinite program. After discretization by the finite element method the latter problem can be solved using a nonlinear SDP code. The article is concluded by a few numerical studies.},
author = {Gaile, Stefanie and Leugering, Günter and Stingl, Michael},
booktitle = {Proceedings of the 23rd IFIP TC 7 Conference on System Modelling and Optimization},
date = {2007-07-23/2007-07-27},
faupublication = {yes},
month = {Jan},
pages = {239-250},
peerreviewed = {unknown},
publisher = {Springer Verlag},
title = {{Free} material optimization for plates and shells},
venue = {Cracow},
volume = {312},
year = {2009}
}
@article{faucris.110637824,
abstract = {If a fractional program does not have a unique solution or the feasible set is unbounded, numerical difficulties can occur. By using a prox-regularization method that generates a sequence of auxiliary problems with unique solutions, these difficulties are avoided. Two regularization methods are introduced here. They are based on Dinkelbach-type algorithms for generalized fractional programming, but use a regularized parametric auxiliary problem. Convergence results and numerical examples are presented.},
author = {Gugat, Martin},
doi = {10.1023/A:1021759318653},
faupublication = {no},
journal = {Journal of Optimization Theory and Applications},
keywords = {differential correction method; Dinkelbach algorithm; Generalized fractional programs; ill-posed problems; linear convergence; prox-regularization},
note = {UnivIS-Import:2015-03-05:Pub.1998.nat.dma.lama1.proxre},
pages = {691-722},
peerreviewed = {Yes},
title = {{Prox}-{Regularization} {Methods} for {Generalized} {Fractional} {Programming}},
url = {http://link.springer.com/article/10.1023/A:1021759318653},
volume = {99},
year = {1998}
}
@book{faucris.115716084,
abstract = {Water supply- and drainage systems and mixed water channel systems are networks whose high dynamic is determined and/or affected by consumer habits on drinking water on the one hand and by climate conditions, in particular rainfall, on the other hand. According to their size, water networks consist of hundreds or thousands of system elements. Moreover, different types of decisions (continuous and discrete) have to be taken in the water management. The networks have to be optimized in terms of topology and operation by targeting a variety of criteria. Criteria may for example be economic, social or ecological ones and may compete with each other. The development of complex model systems and their use for deriving optimal decisions in water management is taking place at a rapid pace. Simulation and optimization methods originating in Operations Research have been used for several decades; usually with very limited direct cooperation with applied mathematics. The research presented here aims at bridging this gap, thereby opening up space for synergies and innovation. It is directly applicable for relevant practical problems and has been carried out in cooperation with utility and dumping companies, infrastructure providers and planning offices. A close and direct connection to the practice of water management has been established by involving application-oriented know-how from the field of civil engineering. On the mathematical side all necessary disciplines were involved, including mixed-integer optimization, multi-objective and facility location optimization, numerics for cross-linked dynamic transportation systems and optimization as well as control of hybrid systems. Most of the presented research has been supported by the joint project "Discret continuous optimization of dynamic water systems" of the federal ministry of education and research (BMBF).},
author = {Martin, Alexander and Klamroth, Kathrin and Lang, Jens and Leugering, Günter and Morsi, Antonio and Oberlack, Martin and Ostrowski, Manfred and Rosen, Roland},
faupublication = {yes},
peerreviewed = {Yes},
publisher = {Birkhäuser},
series = {International Series of Numerical Mathematics},
title = {{Mathematical} {Optimization} of {Water} {Networks}},
volume = {162},
year = {2012}
}
@article{faucris.120144024,
abstract = {There are several studies of the boundary controllability of quasi-linear hyperbolic systems where it is assumed that the eigenvalues of the system matrix do not change their signs during the controlled process.
In this paper we consider the flow through a frictionless horizontal rectangular channel that is governed by de St. Venant equations and show that the state can be controlled in finite time from a stationary initial state to a given stationary terminal state in such a way that during this transition, the state stays in the class of C

The objective function that is to be minimized is the maximum of the L-p-norms of the control functions at both boundaries. It is shown that the analytic solution is, in fact, independent of the choice of the p norm that is minimized. So the optimal controls solve a problem of multicriteria optimization, with the L-p-norms as objective functions.}, author = {Gugat, Martin and Leugering, Günter}, faupublication = {yes}, journal = {Computational and Applied Mathematics}, keywords = {optimal control;wave equation;analytic solution;distributed parameter systems;boundary control;robust control; 90C31; 90C34; 49K40}, month = {Jan}, note = {UnivIS-Import:2015-03-09:Pub.2002.nat.dma.lama1.soluti}, pages = {227-244}, peerreviewed = {Yes}, title = {{Solutions} of {L}-p-norm-minimal control problems for the wave equation}, volume = {21}, year = {2002} } @article{faucris.109450484, author = {Jahn, Johannes}, doi = {10.1007/s10589-014-9674-8}, faupublication = {yes}, journal = {Computational Optimization and Applications}, note = {UnivIS-Import:2015-03-09:Pub.2014.nat.dma.pama21.aderiv}, pages = {393 - 411}, peerreviewed = {Yes}, title = {{A} derivative-free descent method in set optimization}, volume = {60}, year = {2015} } @article{faucris.110509124, abstract = {In many decision problems, criteria occur that can be expressed as ratios. The corresponding optimization problems are nonconvex programs of fractional type. In this paper, an algorithm for the numerical solution of these problems is introduced that converges always at superlinear speed. Numerical examples are presented.}, author = {Gugat, Martin}, doi = {10.1287/mnsc.42.10.1493}, faupublication = {no}, journal = {Management Science}, keywords = {Algorithm; Convex Auxiliary Problem; Decision Analysis; Dual Solutions; Generalized Fractional Programs; Multiple Criteria; Superlinear Convergence}, note = {UnivIS-Import:2015-03-05:Pub.1996.nat.dma.lama1.afasta}, pages = {1493-1499}, peerreviewed = {Yes}, title = {{A} {Fast} {Algorithm} for a {Class} of {Generalized} {Fractional} {Programs}}, volume = {42}, year = {1996} } @incollection{faucris.117917844, address = {New York, Basel, Hong Kong}, author = {Langnese, John E. and Leugering, Günter}, booktitle = {Differential Equations with Applications in Biology, Physics, and Engineering}, editor = {Jerome A. Goldstein, Franz Kappel, Wilhelm Schappacher}, faupublication = {no}, isbn = {0-8247-8571-1}, month = {Jan}, pages = {227-239}, peerreviewed = {unknown}, publisher = {Marcel Dekker, Inc.}, series = {A Series of Lecture Notes in Pure and Applied Mathematics}, title = {{UNIFORM} {ENERGY} {DECAY} {OF} {A} {CLASS} {OF} {CANTILEVERED} {NONLINEAR} {BEAMS} {WITH} {NONLINEAR} {DISSIPATION} {AT} {THE} {FREE} {END}}, volume = {133}, year = {1991} } @article{faucris.106725564, abstract = {

Typically, exact information of the whole subdifferential is not available for intrinsically nonsmooth objective functions such as for marginal functions. Therefore, the semismoothness of the objective function cannot be proved or is even violated. In particular, in these cases standard nonsmooth methods cannot be used. In this paper, we propose a new approach to develop a converging descent method for this class of nonsmooth functions. This approach is based on continuous outer subdifferentials introduced by us. Further, we introduce on this basis a conceptual optimization algorithm and prove its global convergence. This leads to a constructive approach enabling us to create a converging descentmethod. Within the algorithmic framework, neither semismoothness nor calculation of exact subgradients are required. This is in contrast to other approaches which are usually based on the assumption of semismoothness of the

objective function.

},
author = {Knossalla, Martin},
doi = {10.1080/02331934.2018.1426579},
faupublication = {yes},
journal = {Optimization},
keywords = {Mathematical programming; nonsmooth optimization; parametric optimization; variational analysis and optimization},
month = {Jan},
pages = {1-21},
peerreviewed = {Yes},
title = {{Minimization} of marginal functions in mathematical programming based on continuous outer subdifferentials},
year = {2018}
}
@book{faucris.122826924,
address = {Bayreuth},
author = {Rathmann, Wigand},
faupublication = {no},
peerreviewed = {Yes},
publisher = {University of Bayreuth},
series = {Bayreuther Mathematische Schriften},
title = {{Modellierung}, {Simulation} und {Steuerung} von {Netzwerken} schwingender {Balken} mittels dynamischer {Bereichszerlegung}},
volume = {60},
year = {2000}
}
@article{faucris.122946824,
abstract = {We consider the flow of gas through pipelines controlled by a compressor station. Under a subsonic flow assumption we prove the existence of classical solutions for a given finite time interval. The existence result is used to construct Riemannian feedback laws and to prove a stabilization result for a coupled system of gas pipes with a compressor station. We introduce a Lyapunov function and prove exponential decay with respect to the
W

},
author = {Leugering, Günter and Nazarov, Sergei and Schury, Fabian and Stingl, Michael},
doi = {10.1137/110823110},
faupublication = {yes},
journal = {SIAM Journal on Applied Mathematics},
keywords = {asymptotic analysis; Eshelby theorem; optimization; elastic patch; pointwise error estimates; integral and local cost functionals},
pages = {512-534},
peerreviewed = {Yes},
title = {{The} {Eshelby} {Theorem} and {Application} to the optimization of an {Elastic} {Patch}},
volume = {72},
year = {2012}
}
@article{faucris.109756064,
abstract = {We consider the isothermal Euler equations with friction that model the gas flow through pipes. We present a method of time-delayed boundary feedback stabilization to stabilize the isothermal Euler equations locally around a given stationary subcritical state on a finite time interval. The considered control system is a quasilinear hyperbolic system with a source term. For this system we introduce a Lyapunov function with delay terms and develop time-delayed boundary controls for which the Lyapunov function decays exponentially with time. We present the stabilization method for a single gas pipe and for a star-shaped network of pipes.},
author = {Gugat, Martin and Hirsch-Dick, Markus},
doi = {10.3934/mcrf.2011.1.469},
faupublication = {yes},
journal = {Mathematical Control and Related Fields},
keywords = {Boundary control; Conservation law; Delay; Delay term; Euler equations; Feedback stabilization; Feedback with delay; Friction term; Gas network; Hyperbolic PDE; L; Lyapunov function; Riemann invariants; Star-shaped network; Time delay},
note = {UnivIS-Import:2015-03-09:Pub.2011.nat.dma.zentr.timede},
pages = {469-491},
peerreviewed = {Yes},
title = {{Time}-delayed boundary feedback stabilization of the isothermal {Euler} equations with friction},
url = {http://aimsciences.org/journals/contentsListnew.jsp?pubID=483},
volume = {1},
year = {2011}
}
@article{faucris.115216464,
abstract = {This paper presents a reference point approximation algorithm which can be used for the interactive solution of bicriterial nonlinear optimization problems with inequality and equality constraints. The advantage of this method is that the decision maker may choose arbitrary reference points in the criteria space. Moreover, a special tunneling technique is given for the computation of global solutions of certain subproblems. Finally, the proposed method is applied to a mathematical example and a problem in mechanical engineering. © 1992 Plenum Publishing Corporation.},
author = {Jahn, Johannes and Merkel, A.},
doi = {10.1007/BF00939894},
faupublication = {yes},
journal = {Journal of Optimization Theory and Applications},
keywords = {interactive methods; Multi-objective optimization},
note = {UnivIS-Import:2015-03-05:Pub.1992.nat.dma.pama21.refere},
pages = {87-103},
peerreviewed = {Yes},
title = {{Reference} {Point} {Approximation} {Method} for the {Solution} of {Bicriterial} {Nonlinear} {Optimization} {Problems}},
volume = {74},
year = {1992}
}
@article{faucris.117420424,
abstract = {We investigate the evolution and propagation of cracks in 2-d elastic domains, which are subjected to quasi-static loading scenarios. In addition to the classical variational formulation, where the standard potential energy is minimized over the cracked domain under physical conditions characterizing the behavior of the material close to the crack (e.g. non-penetration conditions), we include a 'cohesive traction term' in the energy expression. In this way we obtain a mathematically concise set of partial differential equations with non-linear boundary conditions at the crack interfaces. We perform a finite element discretization using a combination of standard continuous finite elements and so-called cohesive elements. During the simulation process cohesive elements are adaptively inserted at positions where a certain stress bound is exceeded. In our numerical studies we consider domains consisting of a matrix material with fiber inclusions. Beyond pure crack path simulation, our ultimate goal is to determine an optimal shape of the fibers resulting in a crack path that releases for a given load scenario as much energy as possible without destroying the specimen completely. We develop a corresponding optimization model and propose a solution algorithm for the same. The article is concluded by numerical results. © 2011 Elsevier Ltd.},
author = {Prechtel, Marina and Leugering, Günter and Steinmann, Paul and Stingl, Michael},
doi = {10.1016/j.engfracmech.2011.01.007},
faupublication = {yes},
journal = {Engineering Fracture Mechanics},
keywords = {Cohesive zone modeling; Crack growth; Fiber reinforced material; Shape optimization},
note = {UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.toward},
pages = {944-960},
peerreviewed = {Yes},
title = {{Towards} optimization of crack resistance of composite materials by adjustment of fiber shapes},
volume = {78},
year = {2011}
}
@article{faucris.110327624,
author = {Jahn, Johannes},
faupublication = {yes},
journal = {Mathematical Methods of Operations Research},
note = {UnivIS-Import:2015-03-05:Pub.1991.nat.dma.pama21.specia},
pages = {175-265},
peerreviewed = {Yes},
title = {{Special} {Issue} on {Vector} {Optimization}},
volume = {35},
year = {1991}
}
@article{faucris.216448800,
author = {Pflug, Lukas and Keimer, Alexander},
doi = {10.1016/j.jmaa.2019.03.063},
faupublication = {yes},
journal = {Journal of Mathematical Analysis and Applications},
keywords = {Convergence of the nonlocal model to corresponding local model; LWR PDE; Entropy solution; Traffic flow modelling; Nonlocal balance laws},
pages = {1927-1955},
peerreviewed = {Yes},
title = {{On} approximation of local conservation laws by nonlocal conservation laws},
volume = {475},
year = {2019}
}
@incollection{faucris.118371924,
address = {Wiesbaden},
author = {Jahn, Johannes},
booktitle = {Multi-Criteria- und Fuzzy-Systeme in Theorie und Praxis},
editor = {W. Habenicht, B. Scheubrein, R. Scheubrein},
faupublication = {yes},
note = {UnivIS-Import:2015-04-20:Pub.2003.nat.dma.pama21.grundl},
pages = {37-71},
peerreviewed = {unknown},
publisher = {DUV Gabler Edition Wissenschaft},
title = {{Grundlagen} der {Mengenoptimierung}},
year = {2003}
}
@article{faucris.201253582,
author = {Gugat, Martin and Rosier, Lionel and Perrolaz, Vincent},
doi = {10.1007/s00028-018-0449-z},
faupublication = {yes},
journal = {Journal of Evolution Equations},
peerreviewed = {Yes},
title = {{Boundary} stabilization of quasilinear hyperbolic systems of balance laws: exponential decay for small source terms},
url = {https://link.springer.com/article/10.1007/s00028-018-0449-z},
year = {2018}
}
@book{faucris.109061964,
address = {Berlin},
editor = {Jahn, Johannes and Krabs, W.},
faupublication = {yes},
note = {UnivIS-Import:2015-05-08:Pub.1987.nat.dma.pama21.dualit},
publisher = {Springer},
title = {{Recent} {Advances} and {Historical} {Development} of {Vector} {Optimization}},
year = {1987}
}
@article{faucris.107387104,
abstract = {The goal of this paper is to formulate and solve free material optimization problems with constraints on the smallest eigenfrequency of the optimal structure. A natural formulation of this problem as a linear semidefinite program turns out to be numerically intractable. As an alternative, we propose a new approach, which is based on a nonlinear semidefinite low-rank approximation of the semidefinite dual. We introduce an algorithm based on this approach and analyze its convergence properties. The article is concluded by numerical experiments proving the effectiveness of the new approach},
author = {Stingl, Michael and Kocvara, Michal and Leugering, Günter},
doi = {10.1137/080717122},
faupublication = {yes},
journal = {SIAM Journal on Optimization},
pages = {524--547},
peerreviewed = {Yes},
title = {{Free} {Material} {Optimization} with {Fundamental} {Eigenfrequency} {Constraints}},
volume = {20},
year = {2009}
}
@misc{faucris.115699584,
author = {Geißler, Björn and Kolb, Oliver and Lang, Jens and Leugering, Günter and Martin, Alexander and Morsi, Antonio},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Mixed} {Integer} {Linear} {Models} for the {Optimization} of {Dynamical} {Transport} {Networks}},
year = {2010}
}
@article{faucris.117905084,
abstract = {Distributed load control of motions governed by an abstract partial integrodifferential equation is studied. First a new system-theoretic approach to a mild solution theory of equations arising in viscoelasticity of fading memory type is developed. Then it is shown that control results for the damped abstract wave equation devolve to a special class of “virgin” material with fading memory.},
author = {Leugering, Günter},
doi = {10.1080/00036818408839521},
faupublication = {no},
journal = {Applicable Analysis},
keywords = {93B05; 45K05; 73K05},
month = {Jan},
pages = {221-243},
peerreviewed = {Yes},
title = {{EXACT} {CONTROLLABILITY} {IN} {VISCOELASTICITY} {OF} {FADING} {MEMORY} {TYPE}},
url = {http://www.tandfonline.com/doi/abs/10.1080/00036818408839521},
volume = {18},
year = {1984}
}
@article{faucris.110283844,
abstract = {In this paper the multiple regression analysis is considered. The regression coefficients obtained by this method are examined with respect to their numerical stability. With simple stability considerations a criteria is given which can be used if an estimator is to evaluate. © 1981 Phydica-Verlag.},
author = {Jahn, Johannes},
doi = {10.1007/BF01902874},
faupublication = {yes},
journal = {Metrika},
note = {UnivIS-Import:2015-03-05:Pub.1981.nat.dma.pama21.zurbew},
pages = {23-33},
peerreviewed = {Yes},
title = {{Zur} {Bewertung} von {Schätzungen} bei der gewöhnlichen {Regressionsanalyse}},
volume = {28},
year = {1981}
}
@article{faucris.110644424,
abstract = {The generalized contingent epiderivative of set-valued maps is introduced in this paper and its relationship to the contingent epiderivative is investigated. A unified necessary and sufficient optimality condition is derived in terms of the generalized contingent epiderivative. The existence of weak subgradients of set-valued maps is proved, and a sufficient optimality condition of set-valued optimization problems is obtained in terms of weak subgradients.},
author = {Jahn, Johannes and Chen, G.Y.},
faupublication = {yes},
journal = {Mathematical Methods of Operations Research},
keywords = {Generalized contingent epiderivative; Optimality conditions; Set-valued optimization; Subgradient},
note = {UnivIS-Import:2015-03-05:Pub.1998.nat.dma.pama21.optima},
pages = {187-200},
peerreviewed = {Yes},
title = {{Optimality} {Conditions} for {Set}-{Valued} {Optimization} {Problems}},
volume = {48},
year = {1998}
}
@article{faucris.112240964,
abstract = {In this paper, we first define a T-cone which is a unified version of several cones, namely, contingent cone, radial cone, C-tangent cone, Clarke tangent cone, S-cone, adjacent cone, etc. Then, we define the T-epiderivative of a set-valued map which includes the contingent epiderivative, radial epiderivative, S-epiderivative, adjacent epiderivative etc. as special cases. We present several properties of such an epiderivative. The generalized vector T-variational inequality problem is also considered. We provide necessary and sufficient conditions for a solution of a set optimization problem. Several existence results for solutions of set optimization problems and a generalized vector T-variational inequality problem are given.},
author = {Jahn, Johannes and Ansari, Q.H.},
faupublication = {yes},
journal = {Taiwanese Journal of Mathematics},
keywords = {Contingent epiderivative; Existence results; Generalized vector t-variational inequality problems; Optimality conditions; Radial epiderivative; Sepiderivative; T-cone; T-epiderivative; Vector optimization problem},
note = {UnivIS-Import:2015-03-09:Pub.2010.nat.dma.pama21.tepide},
pages = {2447-2468},
peerreviewed = {Yes},
title = {{T}-epiderivatives of set-valued maps and its application to set optimization and generalized variational inequalities},
volume = {14},
year = {2010}
}
@article{faucris.122289024,
abstract = {We consider the shape-topological control of a singularly perturbed variational inequality. The geometry-dependent state problem that we address in this paper concerns a heterogeneous medium with a micro-object (defect) and a macro-object (crack) modeled in two dimensions. The corresponding nonlinear optimization problem subject to inequality constraints at the crack is considered within a general variational framework. For the reason of asymptotic analysis, singular perturbation theory is applied, resulting in the topological sensitivity of an objective function representing the release rate of the strain energy. In the vicinity of the nonlinear crack, the antiplane strain energy release rate is expressed by means of the mode-III stress intensity factor that is examined with respect to small defects such as microcracks, holes, and inclusions of varying stiffiness. The result of shape-topological control is useful either for arrests or rise of crack growth.},
author = {Leugering, Günter and Kovtunenko, Viktor},
doi = {10.1137/151003209},
faupublication = {yes},
journal = {SIAM Journal on Control and Optimization},
keywords = {Antiplane stress intensity factor; Crack-defect interaction; Dipole tensor; Nonlinear crack with nonpenetration; Shape-topological control; Singular perturbation; Strain energy release rate; Topological derivative; Variational inequality},
pages = {1329-1351},
peerreviewed = {Yes},
title = {{A} shape-topological control problem for nonlinear crack-defect interaction: {The} antiplane variational model},
volume = {54},
year = {2016}
}
@article{faucris.111290564,
abstract = {We consider a tree-like network of open channels with outflow at the root. Controls are exerted at the boundary nodes of the network except for the root. In each channel, the flow is modelled by the de St. Venant equations. The node conditions require the conservation of mass and the conservation of energy. We show that the states of the system can be controlled within the entire network in finite time from a stationary supercritical initial state to a given supercritical terminal state with the same orientation. During this transition, the states stay in the class of CIn this paper, a new Ansatz for modelling the Baculovirus infection cycle is presented. The base of this model is the cell cycle distribution at the time of infection. It is possible to calculate the growth of the culture and the initiation of virus processing by considering cell cycle distribution. By taking into account the length of the viral genome and the polymerase activity, it is possible to calculate the virus production rate, which underlies a logistic growth. In the present work, a new hypothesis explaining the accelerated death rates of infected cells has been introduced. This assumption provides the possibilities of performing calculation without any fixed time intervals. The simulation was tested by comparing experimental data with the model prediction. Therefore, cell cycle distributions over the culture time and the growth behaviour of infected and non-infected insect cells were measured. A model, Baculovirus coding for GFP was employed for the present investigation, as it allows tracking the infection and determining the effectiveness of the infection, which is highly dependent on the cell density at the time of infection (TOI). Furthermore, the new model is is taken to simulate data gained from literature about virus release and adsorption. The new assumptions make the model more independent to fit into different cultivation systems.

}, author = {Lindenberger, Christoph and Pflug, Lukas and Hübner, Holger and Buchholz, Rainer}, doi = {10.1007/s12257-011-0371-5}, faupublication = {yes}, journal = {Biotechnology and Bioprocess Engineering}, keywords = {baculovirus; modelling; insect cells; infection cycle}, pages = {211-217}, peerreviewed = {Yes}, title = {{A} novel model for studying baculovirus infection process}, url = {http://link.springer.com/article/10.1007/s12257-011-0371-5}, volume = {17}, year = {2012} } @article{faucris.107368844, abstract = {We consider the in-plane motion of elastic strings on tree-like network, observed from the ‘leaves’. We investigate the inverse problem of recovering not only the physical properties, i.e. the ‘optical lengths’ of each string, but also the topology of the tree which is represented by the edge degrees and the angles between branching edges. To this end we use the Boundary Control method for wave equations on graphs established in [4, 7]. It is shown that under generic assumptions the inverse problem can be solved by applying measurements at all leaves, the root of the tree being fixed.}, author = {Avdonin, Sergei and Leugering, Günter and Mikhaylov, Victor}, doi = {10.1002/zamm.200900295}, faupublication = {yes}, journal = {ZAMM - Zeitschrift für angewandte Mathematik und Mechanik}, pages = {136--150}, peerreviewed = {Yes}, title = {{On} an inverse problem for tree-like networks of elastic strings}, volume = {90}, year = {2010} } @misc{faucris.109715804, abstract = {New images of a three-dimensional scene can be generated from known image sequences using lightfields. To get high quality images, it is important to have accurate information about the structure of the scene. In order to optimize this information, we define a residual-function. This function represents the difference between an image, rendered in a known view from neighboured images and the original image at the same position. In order to get optimal results, we minimize the residual-function by defining a nonlinear least-squares problem, which is solved by an appropriate optimization method. We use a nonmonotone variant of the Levenberg-Marquardt method.}, author = {Hopfgartner, Christian and Scholz, Ingo and Gugat, Martin and Leugering, Günter and Hornegger, Joachim}, faupublication = {yes}, keywords = {Nonlinear Optimization; Imaging; Rendering; Nonmonotone Levenberg-Marquardt; 90C30; 68U10; 94A08}, peerreviewed = {automatic}, title = {{Intensity} based {Three}-{Dimensional} {Reconstruction} with {Nonlinear} {Optimization}}, url = {http://www.am.uni-erlangen.de/de/preprints2000.html}, year = {2007} } @incollection{faucris.118835024, address = {Ilmenau}, author = {Jahn, Johannes}, booktitle = {27. Internationales Wissenschaftliches Kolloquium 1982}, editor = {G. Linnemann}, faupublication = {no}, note = {UnivIS-Import:2015-04-17:Pub.1982.nat.dma.pama21.dualit}, pages = {7-9}, peerreviewed = {unknown}, publisher = {Technische Hochschule Ilmenau}, title = {{Dualität} in der {Vektoroptimierung} mit {Anwendung} in der vektoriellen {Approximation}}, volume = {5}, year = {1982} } @inproceedings{faucris.118501504, abstract = {We consider the feedback stabilization of quasilinear hyperbolic systems on star-shaped networks. We present boundary feedback controls with varying delays. The delays are given by C