Characterization of Solutions of Nonsmooth Variational Problems and Duality

Abstract

In this paper, we introduce a new class of nonsmooth pseudo-invex and nonsmooth quasi-invex functions to non-smooth variational problems. By using these concepts, numbers of necessary and sufficient conditions are established for a nonsmooth variational problem wherein Clarke’s generalized gradient is used. Also, weak, strong and converse duality are established. Keywords—Variational problem; Nonsmooth pseudo-invex; Nonsmooth quasi-invex; Critical point; Duality