Variable metric quasi-Fejér monotonicity

The notion of quasi-Fejér monotonicity has proven to be an efficient tool to simplify and unify the convergence analysis of various algorithms arising in applied nonlinear analysis. In this paper, we extend this notion in the context of variable metric algorithms, whereby the underlying norm is allo...

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Bibliographic Details
Published in	Nonlinear analysis Vol. 78; pp. 17 - 31
Main Authors	Combettes, Patrick L., Vũ, Bằng C.
Format	Journal Article
Language	English
Published	Elsevier Ltd 01.02.2013 Elsevier
Subjects	Algorithms Convergence Convex feasibility problem Convex optimization Hilbert space Inverse problems Mathematics Nonlinearity Norms Optimization Optimization and Control Proximal Landweber method Proximal point algorithm Quasi-Fejér sequence Variable metric Proximal Landweber method 65J05 Convex feasibility problem Inverse problems 90C25 Convex optimization 47H09 Variable metric Hilbert space Quasi-Fejér sequence Proximal point algorithm quasi-Fejér sequence inverse problems convex optimization convex feasibility problem proximal Landweber method proximal point algorithm variable metric Mathematics Subject Classifications 65J05
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ISSN	0362-546X 1873-5215 1873-5215
DOI	10.1016/j.na.2012.09.008

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Summary:	The notion of quasi-Fejér monotonicity has proven to be an efficient tool to simplify and unify the convergence analysis of various algorithms arising in applied nonlinear analysis. In this paper, we extend this notion in the context of variable metric algorithms, whereby the underlying norm is allowed to vary at each iteration. Applications to convex optimization and inverse problems are demonstrated.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0362-546X 1873-5215 1873-5215
DOI:	10.1016/j.na.2012.09.008