Second-order global optimality conditions for convex composite optimization

In recent years second-order sufficient conditions of an isolated local minimizer for convex composite optimization problems have been established. In this paper, second-order optimality conditions are obtained of a globalminimizer for convex composite problems with a nonfinite valued convex function and a twice strictly differentiable function by introducing a generalized representation condition. This result is applied to a minimization problem with a closed convex set constraint which is shown to satisfy the basic constraint qualification. In particular, second-order necessary and sufficient conditions of a solution for a variational inequality problem with convex composite inequality constraints are obtained. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

• Type: Journal
• Year: 1998
• Where: MP
• Authors: Xiaoqi Yang
• Keywords: Convex Composite, Convex Composite Optimization, MP 1998, Sufficient Conditions