Robust minimax optimization problems with applications (Nonlinear Analysis and Convex Analysis)

Abstract

In this paper, we study the optimality conditions and duality in minimax programming problems in the face of data uncertainty. Following the robust optimization approach (worst-case approach), we formulate its robust counterpart of the minimax programming problems under data uncertainty. A representation of the normal cone to a convex set is established under the robust characteristic cone constraint qualification. Then, by using the obtained result, we propose the necessary condition for optimal solutions of the considered problem; moreover, a dual problem in term of Wolfe type to the primal one is stated; and weak and strong duality relations between them are explored. Finally, some of these results are applied to a robust multiobjective optimization problem.