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Bücher Englische Bücher Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization
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Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization
D. Butnariu, A.N. Iusem (Broschiert, Englisch)
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Beschreibung
The aim of this work is to present in a unified approach a series of results concerning totally convex functions on Banach spaces and their applications to building iterative algorithms for computing common fixed points of mea surable families of operators and optimization methods in infinite dimen sional settings. The notion of totally convex function was first studied by Butnariu, Censor and… Reich [31] in the context of the space lRR because of its usefulness for establishing convergence of a Bregman projection method for finding common points of infinite families of closed convex sets. In this finite dimensional environment total convexity hardly differs from strict convexity. In fact, a function with closed domain in a finite dimensional Banach space is totally convex if and only if it is strictly convex. The relevancy of total convexity as a strengthened form of strict convexity becomes apparent when the Banach space on which the function is defined is infinite dimensional. In this case, total convexity is a property stronger than strict convexity but weaker than locally uniform convexity (see Section 1.3 below). The study of totally convex functions in infinite dimensional Banach spaces was started in [33] where it was shown that they are useful tools for extrapolating properties commonly known to belong to operators satisfying demanding contractivity requirements to classes of operators which are not even mildly nonexpansive. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
14.10.2012
Sprache
Englisch
EAN
9789401057882
Herausgeber
Springer Netherland
Serien- oder Bandtitel
Applied Optimization
Sonderedition
Nein
Autor
D. Butnariu, A.N. Iusem
Seitenanzahl
205
Einbandart
Broschiert
Schlagwörter
Banach Space, Convexity, Dimension, Integral equation, Optimal control, algorithms, control, functional analysis, linear optimization, optimization, quality
Thema-Inhalt
PBU - Optimierung
PBM - Geometrie
PBD - Diskrete Mathematik
PBKF - Funktionalanalysis und Abwandlungen
PBKL - Integralrechnung und -gleichungen
Höhe
240 mm
Breite
16 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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