Convex Analysis and Variational Problems

by Ekeland, Ivar; Temam, Roger

• ISBN13: 9780898714500
• ISBN10: 0898714508
• Format: Paperback
• Copyright: 1999-11-01
• Publisher: Society for Industrial & Applied

Summary

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

Preface to the Classics Edition	ix
Preface	xi
PART ONE FUNDAMENTALS OF CONVEX ANALYSIS
Convex functions	3	(31)
Minimization of convex functions and variational inequalities	34	(12)
Duality in convex optimization	46	(29)
PART TWO DUALITY AND CONVEX VARIATIONAL PROBLEMS
Applications of duality to the calculus of variations (I)	75	(41)
Applications of duality to the calculus of variations (II): problems of the type minimal hypersurfaces	116	(49)
Duality by the minimax theorem	165	(21)
Other applications of duality	186	(45)
PART THREE RELAXATION AND NON-CONVEX VARIATIONAL PROBLEMS
Existence of solutions for variational problems	231	(32)
Relaxation of non-convex variational problems (I)	263	(34)
Relaxation of non-convex variational problems (II)	297	(60)
Appendix I. An a priori estimate in non-convex programming	357	(18)
Appendix II. Non-convex optimization problems depending on a parameter	375	(10)
Comments	385	(6)
Bibliography	391	(11)
Index	402