عنوان

Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization

شابک

9789401057882

شابک

9789401140669

شماره

b408819

عنوان اصلي

Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization

نام عام مواد

[Book]

نام نخستين پديدآور

by Dan Butnariu, Alfredo N. Iusem.

محل نشرو پخش و غیره

Dordrecht :

نام ناشر، پخش کننده و غيره

Imprint: Springer,

تاریخ نشرو بخش و غیره

2000.

عنوان فروست

Applied Optimization,

مشخصه جلد

40

شاپا ي ISSN فروست

1384-6485 ;

متن يادداشت

1: Totally Convex Functions -- 1.1. Convex Functions and Bregman Distances -- 1.2. The Modulus of Total Convexity -- 1.3. Total Versus Locally Uniform Convexity -- 1.4. Particular Totally Convex Functions -- 2: Computation of Fixed Points -- 2.1. Totally Nonexpansive Operators -- 2.2. Totally Nonexpansive Families of Operators -- 2.3. Stochastic Convex Feasibility Problems -- 2.4. Applications in Particular Banach Spaces -- 3: Infinite Dimensional Optimization -- 3.1. A Proximal Point Method -- 3.2. Convergence of the Proximal Point Method -- 3.3. The Basics of a Duality Theory -- 3.4. An Augmented Lagrangian Method -- 3.5. Unconstrained Convex Minimization.

بدون عنوان

0

متن يادداشت

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.

شماره استاندارد بين المللي کتاب و موسيقي

9789401057882

عنوان

Springer eBooks

موضوع مستند نشده

Discrete groups.

موضوع مستند نشده

Functional analysis.

موضوع مستند نشده

Integral equations.

موضوع مستند نشده

Mathematical optimization.

موضوع مستند نشده

Mathematics.

موضوع مستند نشده

Operator theory.

مستند نام اشخاص تاييد نشده

Butnariu, Dan.

مستند نام اشخاص تاييد نشده

Iusem, Alfredo N.

مستند نام تنالگان تاييد نشده

SpringerLink (Online service)

تاريخ عمليات

20190307162800.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y