LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	515.64
Title	Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization ([EBook] /) / by Dan Butnariu, Alfredo N. Iusem.
Author	Butnariu, Dan
Added Personal Name	Iusem, Alfredo N. author.
Other name(s)	SpringerLink (Online service)
Publication	Dordrecht : : Springer Netherlands : : Imprint: Springer, , 2000.
Physical Details	XVI, 205 p. : online resource.
Series	Applied Optimization 1384-6485 ; ; 40
ISBN	9789401140669
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-94-011-4066-9
Links to Related Works	Subject References: Calculus of variations . Calculus of variations and optimal control; optimization . Convex and Discrete Geometry . Convex geometry . Discrete geometry . Functional Analysis . Integral Equations . Mathematics . Operator Theory . Authors: Butnariu, Dan . Iusem, Alfredo N. . Corporate Authors: SpringerLink (Online service) . Series: Applied Optimization . Classification: 515.64 .

Catalogue Display

Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization

Reviews