Nonsmooth semi-infinite programming problems with mixed constraints

Abstract

We consider a nonsmooth semi-infinite programming problem with a feasible set defined by inequality and equality constraints and a set constraint. First, we study some alternative theorems which involve linear and sublinear functions and a convex set and we propose several generalizations of them. Then, alternative theorems are applied to obtain, under different constraint qualifications, several necessary optimality conditions in the type of Fritz-John and Karush-Kuhn-Tucker. © 2008 Elsevier Inc. All rights reserved.