APPROXIMATES SOLUTIONS IN ROBUST MINIMAX PROGRAMMING PROBLEMS WITH APPLICATIONS

This paper is devoted to the study of approximate optimality conditions and duality in robust minimax optimzaion problem under a suitable constraint qualification. Using some advanced tools of variational analysis and generalized differentiation, we establish necessary conditions for approximate solutions of a robust minimax optimization problem. Sufficient conditions for such solutions to the considered problem are also provided by generalized convex functions. We state a dual problem to the primal one and explore weak, strong and converse duality relations between them. Finally, by using the obtained results, we derive necessary and sufficient conditions for weak approximate Pareto solutions to the robust multi-objective optimization problem.