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Moreau’s decomposition in Banach spaces

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Abstract

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.

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Acknowledgment

The authors thank one of the referees for making some valuable comments.

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Authors and Affiliations

  1. Laboratoire Jacques-Louis Lions, UMR CNRS 7598, UPMC Université Paris 06, 75005 , Paris, France

    Patrick L. Combettes

  2. Institute of Mathematics, University of the Philippines, 1101 , Diliman, Quezon City, Philippines

    Noli N. Reyes

Authors
  1. Patrick L. Combettes
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  2. Noli N. Reyes
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Correspondence to Patrick L. Combettes.

Additional information

The work of P. L. Combettes was supported by the Agence Nationale de la Recherche under grant ANR-08-BLAN-0294-02.

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Combettes, P.L., Reyes, N.N. Moreau’s decomposition in Banach spaces. Math. Program. 139, 103–114 (2013). https://doi.org/10.1007/s10107-013-0663-y

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  • DOI: https://doi.org/10.1007/s10107-013-0663-y

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