Optimality conditions in convex optimization with locally Lipschitz constraints

In this paper, we consider a convex optimization problem with locally Lipschitz inequality constraints. The KKT optimality conditions (both necessary and sufficient) for quasi ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}-solutions are established under Slater’s constraint qualification and a non-degeneracy condition. Moreover, we explore the optimality condition for weakly efficient solutions in multiobjective convex optimization involving locally Lipschitz constraints. Some examples are given to illustrate our results.