On Second-order Properties of the Moreau-Yosida Regularization for Constrained Nonsmooth Convex Programs

Abstract

In this paper, we investigate a class of constrained nonsmooth convex optimization problems, that is, piecewise C² convex objectives with smooth convex inequality constraints. By using the Moreau-Yosida regularization, we convert these problems into unconstrained smooth convex programs. Then, we investigate the second-order properties of the Moreau-Yosida regularization eta. By introducing the (GAIPCQ) qualification, we show that the gradient of the regularized function eta is piecewise smooth, thereby, semismooth