Moreau's Decomposition in Banach Spaces

2011/03/16 by Patrick L. Combettes, Combettes, Patrick L., Noli N. Reyes +1 · 4 citations
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques #math.FA

paper · pdf · doi:10.48550/arxiv.1103.3178

openalex publication_date 2011/03/16 · arxiv created 2011/04/29 · arxiv updated 2011/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Metric and Generalized Projection Operators in Banach Spaces: Properties\n and Applications

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