Variable metric quasi-Fejér monotonicity

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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Veröffentlicht in:Nonlinear analysis 2013-02, Vol.78, p.17-31
Hauptverfasser: Combettes, Patrick L., Vũ, Bằng C.
Format: Artikel
Sprache:eng
Schlagworte:
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
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Beschreibung
Zusammenfassung: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.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2012.09.008