On optimality conditions in robust optimization problems with locally Lipschitz constraints (Study on Nonlinear Analysis and Convex Analysis)

This paper is based on the published one "Approximate optimality conditions for robust convex optimization without convexity of constraints. Linear and Nonlinear Analysis 5 (2019), no.1, 173-182" written by Z. Hong, L.G. Jiao and D.S. Kim.In this paper, we study a convex optimization problem which minimizes a convex function over a convex feasible set defined by finitely many locally Lipschitz constraints (not necessarily convex or differentiable) in the face of data uncertainty. Under a non-degeneracy condition and the Slater constraint qualification, we present Karush-Kuhn-Tucker optimality conditions for the robust convex optimization problem. Moreover, we apply the obtained results to study the KKT optimality conditions for a quasi E-solution to the robust convex optimization problem