Article ID: | iaor19992587 |
Country: | Netherlands |
Volume: | 81 |
Issue: | 3 |
Start Page Number: | 327 |
End Page Number: | 347 |
Publication Date: | May 1998 |
Journal: | Mathematical Programming |
Authors: | Yang X.Q. |
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 global minimizer for convex composite problems with a non-finite 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.