Epi-convergence Properties of Smoothing by Infimal Convolution

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• 作者：James V. Burke ; Tim Hoheisel
• 关键词：Infimal convolution ; Coercivity ; Epi ; convergence ; Smoothing ; Convex ; composite ; Attouch’s theorem
• 刊名：Set-Valued and Variational Analysis
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：25
• 期：1
• 页码：1-23
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis; Probability Theory and Stochastic Processes;
• 出版者：Springer Netherlands
• ISSN：1877-0541
• 卷排序：25

文摘

This paper concerns smoothing by infimal convolution for two large classes of functions: convex, proper and lower semicontinous as well as for (the nonconvex class of) convex-composite functions. The smooth approximations are constructed so that they epi-converge (to the underlying nonsmooth function) and fulfill a desirable property with respect to graph convergence of the gradient mappings to the subdifferential of the original function under reasonable assumptions. The close connection between epi-convergence of the smoothing functions and coercivity properties of the smoothing kernel is established.