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Description
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.
Keywords: convex analysis, relaxation, non-convex, variational problems, duality, minimax theorem
Table of Contents
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Front Matter
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- PART ONE FUNDAMENTALS OF CONVEX ANALYSIS
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1. Convex Functions
- PART TWO DUALITY AND CONVEX VARIATIONAL PROBLEMS
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4. Applications of Duality to the Calculus of Variations (I)
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7. Other Applications of Duality
- PART THREE RELAXATION AND NON-CONVEX VARIATIONAL PROBLEMS
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8. Existence of Solutions for Variational Problems
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Back Matter
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Excerpt
This edition of the book is the same as the initial one, except for a few corrections and the addition of a small number of references.
Several parts of the book cover basic material which turns out to be useful in a number of applications and which is not expected to evolve; as far as we know this material has not appeared elsewhere in book form since it was published in this book.
©1999 SIAM
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