ON CONSTRAINT QUALIFICATIONS AND OPTIMALITY CONDITIONS IN LOCALLY LIPSCHITZ MULTIOBJECTIVE PROGRAMMING PROBLEMS

Abstract

In this paper we consider a multiobjective optimization problem with locally Lipschitz functions defined on a Banach space involving inequality, equality and set constraints. Some constraint qualifications in terms of Clarke's generalized gradients and directional derivatives are studied, and necessary and sufficient conditions for efficiency with positive Lagrange multipliers associated with all components of the objective are established.