Convex analysis and variational problems : English language ed. originally published: Amsterdam : North-Holland Pub. Co. ; New York : American Elsevier Pub. Co. [distributor], 1976, in series: Studies in mathematics and its applications ; v. 1

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. 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