On multiobjective semi-infinite programs with vanishing constraints and tangential subdifferentials

The aim of this article is to study a nonsmooth multiobjective semi-infinite programming problem with vanishing constraints (MSIPVC). We introduce the stationary point concept in terms of tangential subdifferentials and establish necessary and sufficient Karush–Kuhn–Tucker optimality conditions under suitable generalized constraint qualifications for efficient and other generalized efficient solutions for the MSIPVC in the sense of tangential subdifferentials. Further, we formulate Wolfe and Mond–Weir type dual problems and establish duality relations under convexity and generalized convexity assumptions in presence of tangentially convex functions. We also provide some examples that illustrate our results.