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

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• 作者：Fanwen Meng ; Defeng Sun and Gongyun Zhao
• 关键词：Semismooth ; Generalized Equations ; Moreau ; Yosida Regularization
• 刊名：Mathematical Programming
• 出版年：2005
• 出版时间：November 2005
• 年：2005
• 卷：104
• 期：2-3
• 页码：561-581
• 全文大小：214 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Calculus of Variations and Optimal Control
  Mathematics of Computing
  Numerical Analysis
  Combinatorics
  Mathematical and Computational Physics
  Mathematical Methods in Physics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1436-4646

文摘

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.