Multi-Objective Regularization Robustness

Whenever values of decision variables can not be put into practice exactly, we en-counter variable uncertainty in optimization problems. We present a robust optimization concept to handle variable uncertainty in multi-objecive optimization problems, which we call regularization robust efficiency. Thereby, we extend a concept that was introduced by [Lew02] for single-objective optimization. Furthermore, we show that our concept is closely related to minmax robust efficiency by [EIS14] and set-valued optimization of supremal sets in the sense of [Nie80] and [Löh11]. We investigate properties of regular-ization robust efficient solutions for special cases of objective functions. In particular, we prove that regularization robust efficient solutions can be found by solving a deter-ministic problem in case of linear objective functions. Moreover, we show how continuity properties transfer from a deterministic problem to its regularized robust counterpart.