Moreau's Decomposition in Banach Spaces
Patrick L. Combettes, Noli N. Reyes
TL;DR
This paper extends Moreau's decomposition, a key tool in nonlinear analysis, from Hilbert spaces to reflexive Banach spaces, broadening its applicability in optimization and applied mathematics.
Contribution
It introduces a generalized form of Moreau's decomposition in reflexive Banach spaces, unifying and enhancing previous results.
Findings
Extended Moreau's decomposition to Banach spaces
Unified existing results in nonlinear analysis
Improved theoretical framework for optimization
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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Taxonomy
TopicsOptimization and Variational Analysis · Advanced Optimization Algorithms Research · Sparse and Compressive Sensing Techniques