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Optimization in Function Spaces: With Stability Considerations in Orlicz Spaces
Hardback

Optimization in Function Spaces: With Stability Considerations in Orlicz Spaces

$517.99
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This title is printed to order. This book may have been self-published. If so, we cannot guarantee the quality of the content. In the main most books will have gone through the editing process however some may not. We therefore suggest that you be aware of this before ordering this book. If in doubt check either the author or publisher’s details as we are unable to accept any returns unless they are faulty. Please contact us if you have any questions.

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

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MORE INFO
Format
Hardback
Publisher
De Gruyter
Country
Germany
Date
17 February 2011
Pages
402
ISBN
9783110250206

This title is printed to order. This book may have been self-published. If so, we cannot guarantee the quality of the content. In the main most books will have gone through the editing process however some may not. We therefore suggest that you be aware of this before ordering this book. If in doubt check either the author or publisher’s details as we are unable to accept any returns unless they are faulty. Please contact us if you have any questions.

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

Read More
Format
Hardback
Publisher
De Gruyter
Country
Germany
Date
17 February 2011
Pages
402
ISBN
9783110250206