2ND-ORDER GLOBAL OPTIMALITY CONDITIONS FOR CONVEX COMPOSITE OPTIMIZATION

In recent years second-order sufficient conditions of an isolated loca l minimizer for convex composite optimization problems have been estab lished. In this paper, second-order optimality conditions are obtained of a global minimizer for convex composite problems with a non-finite valued convex function and a twice strictly differentiable function b y introducing a generalized representation condition. This result is a pplied to a minimization problem with a closed convex set constraint w hich is shown to satisfy the basic constraint qualification. In partic ular, second-order necessary and sufficient conditions of a solution f or a variational inequality problem with convex composite inequality c onstraints are obtained. (C) 1998 The Mathematical Programming Society , Inc. Published by Elsevier Science B.V.