Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization (Applied Optimization)

D. Butnariu/ A.N. Iusem

ISBN 10: 079236287X / ISBN 13: 9780792362876

Published by Kluwer Academic Pub, 2000

About this Item

1st edition. 202 pages. 9.50x6.25x0.75 inches. In Stock.

Seller Inventory # x-079236287X

Bibliographic Details

• Title: Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization (Applied Optimization)
• Publisher: Kluwer Academic Pub
• Publication Date: 2000
• Language: English
• ISBN 10: 079236287X
• ISBN 13: 9780792362876
• Binding: Hardcover
• Condition: Brand New
• Weight: 0.5 kilograms

About this title

Synopsis

The main purpose of this book is to present, in a unified approach, several algorithms for fixed point computation, convex feasibility and convex optimization in infinite dimensional Banach spaces, and for problems involving, eventually, infinitely many constraints. For instance, methods like the simultaneous projection algorithm for feasibility, the proximal point algorithm and the augmented Lagrangian algorithm are rigorously formulated and analyzed in this general setting and shown to be applicable to much wider classes of problems than previously known. For this purpose, a new basic concept, `total convexity', is introduced. Its properties are deeply explored, and a comprehensive theory is presented, bringing together previously unrelated ideas from Banach space geometry, finite dimensional convex optimization and functional analysis. For making our general approach possible we had to improve upon classical results like the Hölder-Minkowsky inequality of L^p. All the material is either new or very recent, and has never been organized in a book.
Audience: This book will be of interest to both researchers in nonlinear analysis and to applied mathematicians dealing with numerical solution of integral equations, equilibrium problems, image reconstruction, optimal control, etc.