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
ISSN:0362-546X, 1873-5215
Online Access:Get full text
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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
DOI:10.1016/j.na.2012.09.008