Infinite Alternative Theorems and Nonsmooth Constraint Qualification Conditions

Abstract

In this paper, some infinite alternative theorems in locally convex vector spaces are proved and some applications of these theorems in optimization theory are addressed. Extensions of constraint qualification conditions, in the absence of differentiability using Clarke’s generalized gradient and Mordukhovich’s subdifferential, in Banach and Asplund spaces are introduced; and relationships between them are established. Some of these relations, are proved using the provided alternative theorems.