Convex analysis and variational problems

Ivar Ekeland, Roger Témam9780898714500, 0898714508

No one working in duality should be without a copy of Convex Analysis and Variational Problems. This book 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. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.

---

Table of contents :
Convex Analysis and Variational Problems……Page 1
CONTENTS……Page 8
PREFACE TO THE CLASSICS EDITION……Page 10
PREFACE……Page 12
PART ONE Fundamentals of Convex Analysis……Page 16
CHAPTER I Convex Functions……Page 18
CHAPTER II Minimization of Convex Functions and Variational Inequalities……Page 49
CHAPTER III Duality in Convex Optimization……Page 61
PART TWO Duality and Convex Variational Problems……Page 88
CHAPTER IV Applications of Duality to the Calculus of Variations (I)……Page 90
CHAPTER V Applications of Duality to the Calculus of Variations (II) Minimal Hypersurface Problems……Page 131
CHAPTER VI Duality by the Minimax Theorem……Page 180
CHAPTER VII Other Applications of Duality……Page 201
PART THREE Relaxation and Non-convex Variational Problems……Page 244
CHAPTER VIII Existence of Solutions for Variational Problems……Page 246
CHAPTER IX Relaxation of Non-convex variational Problems(I)……Page 278
CHAPTER X Relaxation of Non-convex Variational Problems(II)……Page 312
APPENDIX I An a priori Estimate in Non-convex Programming……Page 372
APPENDIX II Non-convex Optimization Problems Depending on a Parameter……Page 390
Comments……Page 400
Bibliography……Page 406
Index……Page 417