Second-order global optimality conditions for convex composite optimization

Second-order global optimality conditions for convex composite optimization

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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:
Abstract:

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.

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