Niklas Hebestreit

joint work with Akhtar A. Khan, Elisabeth Köbis, Christiane Tammer

Existence Theorems and Regularization Methods for Non-coercive Vector Variational and Vector Quasi-Variational Inequalities

In this talk, we present a novel existence result for vector variational inequalities. Since these problems are ill-posed in general, we propose a regularization technique for non-coercive problems which allows to derive existence statements even when the common coercivity conditions in the literature do not hold. For this purpose, we replace our original problem by a family of well-behaving problems and study their relationships. Moreover, we apply our results to generalized vector variational inequalities, multi-objective optimization problems and vector quasi-variational inequalities.

Baasansuren Jadamba

Optimization Based Approaches for the Inverse Problem of Identifying Tumors

This talk focuses on the inverse problem of parameter identification in an incompressible linear elasticity system. Optimization formulations for the inverse problem, a stable identification process using regularization, as well as optimality conditions, will be presented. Results of numerical simulations using synthetic data will be shown.

Ernest Quintana

joint work with Gemayqzel Bouza, Christiane Tammer, Anh Tuan Vu

Fermat's Rule for Set Optimization with Set Relations

In this talk, we consider Set Optimization problems with respect to the set approach. Specifically, we deal with the lower less and the upper less relations. Under convexity and Lipschitz properties of the set valued objective map, we derive corresponding properties for suitable scalarizing functionals. We then obtain upper estimates for Clarke's subdifferential of these functionals. As a consequence of the scalarization approach, we show a Fermat's rule for this class of problems. Ideas for a descent method are also discussed.