Quasi-Gap and Gap Functions for Non-Smooth Multi-Objective Semi-Infinite Optimization Problems

Abstract

In this paper‎, ‎we introduce and study some new single-valued gap functions for non-differentiable semi-infinite multiobjective optimization problems with locally Lipschitz data‎. ‎Since one of the fundamental properties of gap function for optimization problems is its abilities in characterizing the solutions of the problem in question‎, ‎then the essential properties of the newly introduced gap functions are established‎. ‎All results are given in terms of the Clarke subdifferential.