Optimality and duality in nondifferentiable minimax programming problems involving \(\epsilon \)-quasi solutions

The aim of this paper is to study optimality conditions and duality analysis for the \(\epsilon \) $ϵ$ -quasi optimal solutions of nondifferentiable minimax programming problem (NMPP) via the Aubin–Frankowska’s generalized subdifferentials, where \(\epsilon \) $ϵ$ is a non-negative real number. Employing some advanced tools of generalized subdifferentials and regularity conditions, Karush–Kuhn–Tucker-type necessary optimality conditions for \(\epsilon \) $ϵ$ -quasi optimal solutions of problem (NMPP) are established. Under suitable assumptions on the \(\epsilon \) $ϵ$ -pseudoconvexity and \(\epsilon \) $ϵ$ -quasiconvexity, necessary optimality conditions become sufficient optimality conditions. Besides, these results are applied direct to a constrained vector optimization problem. In addition, a Wolfe-type and Mond–Weir-type dual problem to the primal problem is proposed and weak, strong, and converse duality relations among them are explored. Some illustrative examples are provided for our findings.