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

Abstract

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.