Moreau's decomposition in Banach spaces

被引：15

作者：

Combettes, Patrick L. ^{[1
]}

Reyes, Noli N. ^{[2
]}

机构：

[1] Univ Paris 06, UMR CNRS 7598, Lab Jacques Louis Lions, F-75005 Paris, France

[2] Univ Philippines, Inst Math, Quezon City 1101, Philippines

来源：

MATHEMATICAL PROGRAMMING | 2013年 / 139卷 / 1-2期

关键词：

Banach space; Bregman distance; Convex optimization; Infimal convolution; Legendre function; Moreau's decomposition; Proximity operator; ANALYSE FONCTIONNELLE; PROXIMAL MAPPINGS; CONVEX-FUNCTIONS; SIGNAL RECOVERY; CONJUGATE; MINIMIZATION; ALGORITHM; MATRICES;

D O I：

10.1007/s10107-013-0663-y

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

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.

引用

页码：103 / 114

页数：12

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