A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces

A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces

We consider a wide class of iterative methods arising in numerical mathematics and optimization that are known to converge only weakly. Exploiting an idea originally proposed by Haugazeau, we present a simple modification of these methods that makes them strongly convergent without additional assump...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematics of operations research 2001-05, Vol.26 (2), p.248-264
Hauptverfasser: Bauschke, Heinz H., Combettes, Patrick L.
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Approximation
Convergence
Convex feasibility
Equilibrium theory
Fejér-monotonicity
firmly nonexpansive mapping
fixed point
Haugazeau
Hilbert space
Hilbert spaces
Iterative methods
Mathematical functions
Mathematical monotonicity
Mathematical sequences
Mathematics
maximal monotone operator
Operations research
Perceptron convergence procedure
projection
proximal point algorithm
resolvent
Studies
subgradient algorithm
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We consider a wide class of iterative methods arising in numerical mathematics and optimization that are known to converge only weakly. Exploiting an idea originally proposed by Haugazeau, we present a simple modification of these methods that makes them strongly convergent without additional assumptions. Several applications are discussed.
ISSN:0364-765X
1526-5471
DOI:10.1287/moor.26.2.248.10558