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

In this paper, we attempt to 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 n. By introducing the (GAIPCQ) qualification, we show that the gradient of the regularized function n is piecewise smooth, thereby, semismooth. [ABSTRACT FROM AUTHOR]