The Cost of Not Knowing Enough: Mixed-Integer Optimization with Implicit Lipschitz Nonlinearities

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Publication Details

Author(s): Schmidt M, Sirvent M, Wollner W
Publication year: 2018
Language: English


Abstract

It is folklore knowledge that nonconvex mixed-integer nonlinear
optimization problems can be notoriously hard to solve in practice. In
this paper we go one step further and drop analytical properties that
are usually taken for granted in mixed-integer nonlinear optimization.
First, we only assume Lipschitz continuity of the nonlinear functions
and additionally consider multivariate implicit constraint functions
that cannot be solved for any parameter analytically. For this class of
mixed-integer problems we propose a novel algorithm based on an approximation of the feasible set in the domain of the nonlinear
function - in contrast to an approximation of the graph of the function
considered in prior work. This method is shown to compute global optimal
solutions in finite time and we also provide a worst-case iteration
bound. However, first numerical experiences reveal that a lot of work is
still to be done for this highly challenging class of problems and we
thus finally propose some possible directions of future research.


FAU Authors / FAU Editors

Schmidt, Martin Prof. Dr.
Juniorprofessur für Optimierung von Energiesystemen
Sirvent, Mathias
Economics - Discrete Optimization - Mathematics (EDOM)


External institutions with authors

Technische Universität Darmstadt


How to cite

APA:
Schmidt, M., Sirvent, M., & Wollner, W. (2018). The Cost of Not Knowing Enough: Mixed-Integer Optimization with Implicit Lipschitz Nonlinearities.

MLA:
Schmidt, Martin, Mathias Sirvent, and Winnifried Wollner. The Cost of Not Knowing Enough: Mixed-Integer Optimization with Implicit Lipschitz Nonlinearities. 2018.

BibTeX: 

Last updated on 2018-10-08 at 23:54

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