Moreau’s decomposition in Banach spaces

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• 作者：Patrick L. Combettes (1)
  Noli N. Reyes (2)
  
• 关键词：Banach space ; Bregman distance ; Convex optimization ; Infimal convolution ; Legendre function ; Moreau’s decomposition ; Proximity operator ; 49M27 ; 47H05 ; 65K10
• 刊名：Mathematical Programming
• 出版年：2013
• 出版时间：2 - June 2013
• 年：2013
• 卷：139
• 期：1
• 页码：103-114
• 全文大小：180KB
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• 作者单位：Patrick L. Combettes (1)
  Noli N. Reyes (2)
  
  1. Laboratoire Jacques-Louis Lions, UMR CNRS 7598, UPMC Université Paris 06, 75005, Paris, France
  2. Institute of Mathematics, University of the Philippines, 1101, Diliman, Quezon City, Philippines
  
• ISSN：1436-4646

文摘

Moreau’s decomposition is a powerful nonlinear hilbertian analysis tool that has been used in various areas of optimization and applied mathematics. In this paper, it is extended to reflexive Banach spaces and in the context of generalized proximity measures. This extension unifies and significantly improves upon existing results.