D Butnariu

(Author)

Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization (Softcover Reprint of the Original 1st 2000)Paperback - Softcover Reprint of the Original 1st 2000, 14 October 2012

Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization (Softcover Reprint of the Original 1st 2000)
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Part of Series
Applied Optimization
Print Length
205 pages
Language
English
Publisher
Springer
Date Published
14 Oct 2012
ISBN-10
9401057885
ISBN-13
9789401057882

Description

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.

Product Details

Authors:
D ButnariuA N Iusem
Book Edition:
Softcover Reprint of the Original 1st 2000
Book Format:
Paperback
Country of Origin:
NL
Date Published:
14 October 2012
Dimensions:
23.39 x 15.6 x 1.19 cm
ISBN-10:
9401057885
ISBN-13:
9789401057882
Language:
English
Location:
Dordrecht
Pages:
205
Publisher:
Weight:
317.51 gm

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