Optimality conditions and duality analysis via generalized subdifferentials for \(\epsilon \)-quasi solutions of vector optimization problems

The goal of this article is to establish optimality conditions for the \(\epsilon \) $ϵ$ -quasi efficient solutions of constrained vector optimization problem (CVOP) in terms of the Aubin–Frankowska’s generalized subdifferentials, where \(\epsilon \ge 0.\) $ϵ\ge 0.$ We introduce some new versions of the regularity condition of the (RC3-s) types \((s=\overline{1\ldots p})\) $(s=\overline{1\dots p})$ and propose some new concepts of \(\epsilon \) $ϵ$ -pseudoconvexity, \(\epsilon \) $ϵ$ -quasiconvexity and \(\epsilon \) $ϵ$ -quasilinearly for calm functions. After that we derive weak and strong KKT-type necessary and sufficient conditions to such a problem. Additionally, a strong KKT-type necessary optimality condition is applied in order to construct a Mond–Weir-type dual vector optimization problem (MWCVOP). Some weak, strong and converse duality theorems for the primal problem (CVOP) and the dual problem (MWCVOP) are explored under some suitable assumptions on the \(\epsilon \) $ϵ$ -pseudoconvexity and pseudoconvexity. Illustrative examples are also provided for our findings.