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Convex Analysis and Variational Problems

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By Ivar Ekeland and Roger TŽémam

1999 / xiv + 402 pages / Softcover / ISBN: 978-0-898714-50-0 / List Price $73.50 / SIAM Member Price $51.45 / Order Code CL28

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.

Practitioners of duality in such fields as mathematical economy, nonlinear programming, continuum mechanics (solids and fluids), mixed finite elements, and control theory will find this text indispensable. Analysts interested in partial differential equations will also find it useful.

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.

ISBN: 9780898714500

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