Semismoothness of solutions to generalized equations and the Moreau-Yosida regularization

• 成果类型: Article
• 署名作者: Meng, FW; Sun, DF; Zhao, GY
• 署名单位: University of Southampton; National University of Singapore
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-005-0629-9
• 发表日期: 2005
• 页码: 561-581
• 关键词: implicit-function theorem; Newton method; complementarity-problems; valued functions; convex; inverse; CONVERGENCE; MULTIFUNCTIONS; interpolation; matrix

摘要

We show that a locally Lipschitz homeomorphism function is semismooth at a given point if and only if its inverse function is semismooth at its image point. We present a sufficient condition for the semismoothness of solutions to generalized equations over cone reducible (nonpolyhedral) convex sets. We prove that the semismoothness of solutions to the Moreau-Yosida regularization of a lower semicontinuous proper convex function is implied by the semismoothness of the metric projector over the epigraph of the convex function.