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Totally Convex Functions for Fixed Points Computation : Applied Optimization - D. Butnariu

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Totally Convex Functions for Fixed Points Computation

By: D. Butnariu, A.N. Iusem

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Hardcover | 1 May 2000

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Hardcover
224 Pages

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23.39 x 15.6 x 1.42

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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 HAlder-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.

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms Algebra Engineering & Technology Mechanical Engineering & Materials Production & Industrial Engineering Applied Mathematics Medicine Medicine in General Optimisation

Linear Programming Geometry Analytic Geometry

Introduction
Totally Convex Functions
Convex Functions and Bregman Distances	p. 1
The Modulus of Total Convexity	p. 17
Total Versus Locally Uniform Convexity	p. 30
Particular Totally Convex Functions	p. 45
Computation of Fixed Points
Totally Nonexpansive Operators	p. 65
Totally Nonexpansive Families of Operators	p. 79
Stochastic Convex Feasibility Problems	p. 92
Applications in Particular Banach Spaces	p. 109
Infinite Dimensional Optimization
A Proximal Point Method	p. 129
Convergence of the Proximal Point Method	p. 138
The Basics of a Duality Theory	p. 145
An Augmented Lagrangian Method	p. 154
Unconstrained Convex Minimization	p. 171
Bibliography	p. 189
Index	p. 201
Table of Contents provided by Blackwell. All Rights Reserved.

Totally Convex Functions for Fixed Points Computation

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Hardcover

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