Title: Subdifferentials and Lipschitz properties of translation invariant functionals and applications

Speaker: Christiane Tammer (MLU)

Date and Time: September 9th, 2020, 17:00 AEST (Register here for remote connection via Zoom)

Abstract: In the talk, we are dealing with translation invariant functionals and their application for deriving necessary conditions for minimal solutions of constrained and unconstrained optimization problems with respect to general domination sets.

Translation invariant functionals are a natural and powerful tool for the separation of not necessarily convex sets and scalarization. There are many applications of translation invariant functionals in nonlinear functional analysis, vector optimization, set optimization, optimization under uncertainty, mathematical finance as well as consumer and production theory.

The primary objective of this talk is to establish formulas for basic and singular subdifferentials of translation invariant functionals and to study important properties such as monotonicity, the PSNC property, the Lipschitz behavior, etc. of these nonlinear functionals without assuming that the shifted set involved in the definition of the functional is convex. The second objective is to propose a new way to scalarize a set-valued optimization problem. It allows us to study necessary conditions for minimal solutions in a very broad setting in which the domination set is not necessarily convex or solid or conical. The third objective is to apply our results to vector-valued approximation problems.

This is a joint work with T.Q. Bao (Northern Michigan University).