Optimality conditions for nonsmooth interval-valued and multiobjective semi-infinite programming

Abstract

We consider a nonsmooth semi-infinite interval-valued vector programming problem, where the objectives and constraint functions need not to be locally Lipschitz. Using Abadie’s constraint qualification and convexificators, we provide Karush–Kuhn–Tucker necessary optimality conditions by converting the initial problem into a bi-criteria optimization problem. Furthermore, we establish sufficient optimality conditions under the asymptotic convexity assumption.