On local quasi efficient solutions for nonsmooth vector optimization

TL;DR

This paper investigates local quasi efficient solutions in nonsmooth vector optimization, introducing new generalized invexity conditions and linking solutions to vector critical points through variational inequalities.

Contribution

It develops necessary and sufficient optimality conditions using Stampacchia and Minty inequalities under generalized invexity assumptions.

Findings

Established optimality conditions based on Clarke's generalized Jacobians.

Linked local quasi weak efficient solutions to vector critical points.

Provided a framework connecting variational inequalities with solution concepts.

Abstract

We are interested in local quasi efficient solutions for nonsmooth vector optimization problems under new generalized approximate invexity assumptions. We formulate necessary and sufficient optimality conditions based on Stampacchia and Minty types of vector variational inequalities involving Clarke's generalized Jacobians. We also establish the relationship between local quasi weak efficient solutions and vector critical points.