WC-05: Variational Methods in Vector and Set Optimization
Stream: Multiobjective Optimization
Room: Pontryagin
Chair(s): César Gutiérrez, Gabriele Eichfelder

Stability of set optimization problems
Ruben Lopez, Elvira Hernández
We study the stability of set optimization problems when the data (feasible sets and objective maps) admit variations. The data vary by means of a variational convergence notion for set-valued maps.

A Vectorization Scheme for Nonconvex Set Optimization Problems
Stefan Rocktäschel, Gabriele Eichfelder, Ernest Quintana
In this talk, we examine a solution approach for set-valued optimization problems with respect to the lower less relation. Thereby, we formulate a parametric vector optimization problem whose solution set approximates, in a specific sense, that of the set-valued optimization problem with arbitrary accuracy. We also investigate particular classes of set-valued mappings for which the corresponding set optimization problem is equivalent to the vector optimization problem. Surprisingly, set-valued mappings with a convex graph are one of the classes for which this equivalence holds.

Ekeland variational principles in vector equilibrium problems
César Gutiérrez
The talk addresses Ekeland variational principles for vector bifunctions defined on complete metric spaces. Several versions of that result are stated via a scalarization approach and new lower semicontinuity and lower boundedness assumptions. As a result, some recent Ekeland variational principles of the literature are improved since weaker hypotheses are assumed.