Necessary and Sufficient Conditions for (Weakly) Efficient of Non-Differentiable Multi-Objective Semi-Infinite Programming Problems

Abstract

We consider a multi-objective semi-infinite programming problem with a feasible set defined by inequality constraints. First, we present a Fritz–John type necessary optimality condition. Then, we introduce two constraint qualifications and derive the weak and strong Karush–Kuhn–Tucker types necessary conditions for (weakly) efficient solution of the considered problem. Finally, an extension of a Caristi–Ferrara–Stefanescu result for the (\(\Phi\), \(\rho\))-invexity is proved, and some sufficient conditions are presented under this weak assumption. All results are given in term of Clarke subdifferential.