Concepts on generalized epsilon-subdifferentials for minimizing locally Lipschitz continuous functions - Knossalla, Martin (Journal of Nonlinear and Variational Analysis, 2017)

Continuous outer subdifferentials in nonsmooth optimization - Knossalla, Martin (Set-Valued and Variational Analysis, 2018)

LAGRANGE THEORY OF DISCRETE-CONTINUOUS NONLINEAR OPTIMIZATION - Jahn, Johannes; Knossalla, Martin (Journal of Nonlinear and Variational Analysis, 2018)
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.
CRIS-Team WoS Importer:2019-04-02

Minimization of marginal functions in mathematical programming based on continuous outer subdifferentials - Knossalla, Martin (Optimization, 2018)
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.
Keywords: Mathematical programming; nonsmooth optimization; parametric optimization; variational analysis and optimization