Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization

Dan Butnariu

ISBN 10: 079236287X / ISBN 13: 9780792362876

Editore: Springer, 2000

Riguardo questo articolo

Druck auf Anfrage Neuware - Printed after ordering - 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 Lp. 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.

Codice articolo 9780792362876

Dati bibliografici

• Titolo: Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization
• Editore: Springer
• Data di pubblicazione: 2000
• Lingua: Inglese
• ISBN 10: 079236287X
• ISBN 13: 9780792362876
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 18 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 18 millimetri di profondità
• Peso: 506 grammi

Descrizione articolo

Riassunto

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 a general approach possible the work aims to improve upon classical results like the Holder-Minkowsky inequality of ℒp. This book should be of interest to both researchers in nonlinear analysis and to applied mathematicians dealing with numerical solution of integral equations, equilibrium problems, image reconstruction, and optimal control.

Contenuti

Introduction. 1. Totally Convex Functions. 2. Computation of Fixed Points. 3. Infinite Dimensional Optimization. Bibliography. Index.