Exponential type vector variational-like inequalities and nonsmooth vector optimization problems

Abstract

This paper is devoted to study a new class of exponential form of vector variational-like inequality problems comprised of locally Lipschitz functions having exponential type invexities. In the setting of Banach space, we investigate the relationship of nonsmooth exponential type vector variational-like inequality problems with vector optimization problems involving nonsmooth \((p,r)\)-invex functions. Also, we explore the conditions for solvability of the aforesaid nonsmooth exponential type vector variational-like inequality problems using Fan-KKM Theorem. Moreover, we provide examples to elucidate our results.