Vector Critical Points and Cone Efficiency in Nonsmooth Vector Optimization

Abstract

In this paper, a nonsmooth vector optimization problem with cone and equality constraints is considered. We establish some relations between the notions of vector critical points in the sense of Fritz John and in the sense of Karush-Kuhn-Tucker and weakly $K$-efficient and $K$-efficient solutions for the constrained vector optimization problem in which every component of the involved functions is locally Lipschitz. These relationships are stated under cone-$FJ$-pseudo-invexity and cone-$KT$-pseudo-invexity hypotheses defined for the considered vector optimization problem with cone inequality and also equality constraints and via the Clarke generalized gradient for vector-valued functions.