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Optimization and Control of Nonsmooth and Complementarity-Based Systems: Theory and Numerics

Organizers:
Gerd Wachsmuth (TU Chemnitz, Germany) and Thomas Surowiec (HU Berlin, Germany)

Abstract:
Given the rising amount of phenomena in telecommunications, economics, image processing, and engineering that can be modeled as complementarity or equilibrium problems, i.e., (quasi)- variational inequalities, both the theoretical study and numerical treatment are of major in- terest. In all of these models, one is provided with several external parameters. The wish to achieve a desired state or to calibrate these parameters according to observations, then leads to optimization problems with complementarity constraints (MPCCs, MPECs), nonsmooth inverse problems, and hierarchical or bilevel optimization problems. Due to a general lack of regularity of the parameter-to- state mappings or the inherent degeneracy with regards to constraint qualifications of complementarity constraints, standard methods of nonlinear programming, optimization in Banach spaces, and optimal control cannot be directly applied to analyze these models or develop ecient numerical methods. Further- more, as many of these models arise from problems involving partial differential equations and associated variational inequalities or they contain distributed/stochastic variables and parameters, the practicioner is often met with an explosion in the number of decision variables upon discretiziation. With this minisymposium, we seek to achieve the following two scientific goals: 1) Define and advance the current forefront of research in complementarity problems and the optimization of complementarity-based systems, e.g., variational inequalities and equilibrium problems. 2) Identify analytical and numerical challenges associated with the focus areas. In addition, we seek to bring together scientists working on both finite and infinite dimensional formulations of these problems so as better ascertain the boundaries of possibility.