Approximate proper efficiencies in nonsmooth semi-infinite multiobjective optimization problems

Abstract

This article is devoted to studying a nonsmooth semi-infinite multiobjective optimization problem (SIMP) in terms of the Mordukhovich/limiting subdifferentials. We first establish necessary and sufficient conditions for an ε -quasi positively properly efficient solution of a problem (SIMP). We also investigate Mond–Weir type dual problems under assumptions of ε -quasi pseudo-generalized convexity. Next, we provide an application to a nonsmooth fractional semi-infinite multiobjective optimization problem. Finally, some examples are given to illustrate the obtained results. The obtained results improve or include some recent known ones.