Convex Analysis and Variational Problems
Published on 30. November 1999
Book
Paperback/Softback
416 pages
978-0-89871-450-0 (ISBN)
Description
No one working in duality should be without a copy of this book. It contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. This SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.
More details
Series
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Product notice
Paperback (trade)
Dimensions
Height: 230 mm
Width: 155 mm
Thickness: 22 mm
Weight
568 gr
ISBN-13
978-0-89871-450-0 (9780898714500)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Content
Preface to the Classics Edition
Preface
Part One: Fundamentals of Convex Analysis. Chapter I: Convex Functions
Chapter II: Minimization of Convex Functions and Variational Inequalities
Chapter III: Duality in Convex Optimization
Part Two: Duality and Convex Variational Problems. Chapter IV: Applications of Duality to the Calculus of Variations (I)
Chapter V: Applications of Duality to the Calculus of Variations (II)
Chapter VI: Duality by the Minimax Theorem
Chapter VII: Other Applications of Duality
Part Three: Relaxation and Non-Convex Variational Problems. Chapter VIII: Existence of Solutions for Variational Problems
Chapter IX: Relaxation of Non-Convex Variational Problems (I)
Chapter X: Relaxation of Non-Convex Variational Problems (II)
Appendix I: An a priori Estimate in Non-Convex Programming
Appendix II: Non-Convex Optimization Problems Depending on a Parameter
Comments
Bibliography
Index.
Preface
Part One: Fundamentals of Convex Analysis. Chapter I: Convex Functions
Chapter II: Minimization of Convex Functions and Variational Inequalities
Chapter III: Duality in Convex Optimization
Part Two: Duality and Convex Variational Problems. Chapter IV: Applications of Duality to the Calculus of Variations (I)
Chapter V: Applications of Duality to the Calculus of Variations (II)
Chapter VI: Duality by the Minimax Theorem
Chapter VII: Other Applications of Duality
Part Three: Relaxation and Non-Convex Variational Problems. Chapter VIII: Existence of Solutions for Variational Problems
Chapter IX: Relaxation of Non-Convex Variational Problems (I)
Chapter X: Relaxation of Non-Convex Variational Problems (II)
Appendix I: An a priori Estimate in Non-Convex Programming
Appendix II: Non-Convex Optimization Problems Depending on a Parameter
Comments
Bibliography
Index.