Variable metric forward-backward splitting with applications to monotone inclusions in duality

We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in duality. Some of these algorithms are new even when speciali...

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Bibliographic Details
Published inOptimization Vol. 63; no. 9; pp. 1289 - 1318
Main Authors Combettes, Patrick L., Vũ, Băng C.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis Group 01.09.2014
Taylor & Francis LLC
Taylor & Francis
Subjects
Algorithms
cocoercive operator
composite operator
demiregularity
duality
forward-backward splitting algorithm
Hilbert space
Mathematical problems
Mathematical programming
Mathematics
monotone inclusion
monotone operator
Optimization and Control
primal-dual algorithm
quasi-Fejér sequence
Studies
variable metric
cocoercive operator
primal-dual algorithm
forward-backward splitting algorithm
demiregularity
variable metric Mathematics Subject Classifications 47H05
duality
monotone operator
90C25
49M29
49M27
composite operator
quasi-Fejér se-quence
monotone inclusion
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Summary:We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in duality. Some of these algorithms are new even when specialized to the fixed metric case. Various applications are discussed.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2012.733883