Robustness of multi-valued optimization problems via set relations (Study on Nonlinear Analysis and Convex Analysis)

Abstract

This paper focuses on the feasibility of multi-valued optimization problems under perturbations. By using set relations and their scalarization, a modified version of theorems of the alternative can characterize the robustness of the feasibility. Especially under some assumptions, we show algorithms for evaluating the robustness which computers could deal with.