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 in:Optimization 2014-09, Vol.63 (9), p.1289-1318
Main Authors: Combettes, Patrick L., Vũ, Băng C.
Format: Article
Language:English
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
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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.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2012.733883