Optimization in function spaces : with stability considerations in Orlicz spaces / Peter Kosmol, Dieter Müller-Wichards.

Format:

Book

Author/Creator:

Kosmol, Peter.

Contributor:

Müller-Wichards, D. (Dieter), 1946-

Series:

De Gruyter series in nonlinear analysis and applications ; 13.

De Gruyter series in nonlinear analysis and applications, 0941-813X ; 13

Language:

English

Subjects (All):

Stability--Mathematical models.

Stability.

Mathematical optimization.

Orlicz spaces.

Physical Description:

1 online resource (404 p.)

Edition:

1st ed.

Place of Publication:

Berlin ; New York : De Gruyter, 2011.

Language Note:

English

Summary:

This is an essentially self-contained book on the theory of convex functions and convex optimization in Banach spaces, with a special interest in Orlicz spaces. Approximate algorithms based on the stability principles and the solution of the corresponding nonlinear equations are developed in this text. A synopsis of the geometry of Banach spaces, aspects of stability and the duality of different levels of differentiability and convexity is developed. A particular emphasis is placed on the geometrical aspects of strong solvability of a convex optimization problem: it turns out that this property is equivalent to local uniform convexity of the corresponding convex function. This treatise also provides a novel approach to the fundamental theorems of Variational Calculus based on the principle of pointwise minimization of the Lagrangian on the one hand and convexification by quadratic supplements using the classical Legendre-Ricatti equation on the other. The reader should be familiar with the concepts of mathematical analysis and linear algebra. Some awareness of the principles of measure theory will turn out to be helpful. The book is suitable for students of the second half of undergraduate studies, and it provides a rich set of material for a master course on linear and nonlinear functional analysis. Additionally it offers novel aspects at the advanced level. From the contents: Approximation and Polya Algorithms in Orlicz Spaces Convex Sets and Convex Functions Numerical Treatment of Non-linear Equations and Optimization Problems Stability and Two-stage Optimization Problems Orlicz Spaces, Orlicz Norm and Duality Differentiability and Convexity in Orlicz Spaces Variational Calculus

Contents:

Front matter

Preface

Contents

1 Approximation in Orlicz Spaces

2 Polya Algorithms in Orlicz Spaces

3 Convex Sets and Convex Functions

4 Numerical Treatment of Non-linear Equations and Optimization Problems

5 Stability and Two-stage Optimization Problems

6 Orlicz Spaces

7 Orlicz Norm and Duality

8 Differentiability and Convexity in Orlicz Spaces

9 Variational Calculus

Bibliography

List of Symbols

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786613166340

9781283166348

1283166348

9783110250213

3110250217

OCLC:

723945523