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Convex Analysis

(PMS-28)

By: Ralph Tyrell Rockafellar

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Paperback | 12 January 1997

At a Glance

Paperback
472 Pages

Dimensions(cm)
22.8 x 15.3 x 2.5

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Available for the first time in paperback, R. Tyrrell Rockafellar's classic study presents readers with a coherent branch of nonlinear mathematical analysis that is especially suited to the study of optimization problems. Rockafellar's theory differs from classical analysis in that differentiability assumptions are replaced by convexity assumptions. The topics treated in this volume include: systems of inequalities, the minimum or maximum of a convex function over a convex set, Lagrange multipliers, minimax theorems and duality, as well as basic results about the structure of convex sets and the continuity and differentiability of convex functions and saddle- functions.

This book has firmly established a new and vital area not only for pure mathematics but also for applications to economics and engineering. A sound knowledge of linear algebra and introductory real analysis should provide readers with sufficient background for this book. There is also a guide for the reader who may be using the book as an introduction, indicating which parts are essential and which may be skipped on a first reading.

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"This book should remain for some years as the standard reference for anyone interested in convex analysis."--J. D. Pryce, Edinburgh Mathematical Society

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms Optimisation Linear Programming Miscellaneous Items

Preface
Introductory Remarks: A Guide for the Reader
Affine Sets	p. 3
Convex Sets and Cones	p. 10
The Algebra of Convex Sets	p. 16
Convex Functions	p. 23
Functional Operations	p. 32
Relative Interiors of Convex Sets	p. 43
Closures of Convex Functions	p. 51
Recession Cones and Unboundedness	p. 60
Some Closedness Criteria	p. 72
Continuity of Convex Functions	p. 82
Separation Theorems	p. 95
Conjugates of Convex Functions	p. 102
Support Functions	p. 112
Polars of Convex Sets	p. 121
Polars of Convex Functions	p. 128
Dual Operations	p. 140
Caratheodory's Theorem	p. 153
Extreme Points and Faces of Convex Sets	p. 162
Polyhedral Convex Sets and Functions	p. 170
Some Applications of Polyhedral Convexity	p. 179
Helly's Theorem and Systems of Inequalities	p. 185
Linear Inequalities	p. 198
Directional Derivatives and Subgradients	p. 213
Differential Continuity and Monotonicity	p. 227
Differentiability of Convex Functions	p. 241
The Legendre Transformation	p. 251
The Minimum of a Convex Function	p. 263
Ordinary Convex Programs and Lagrange Multipliers	p. 273
Bifunctions and Generalized Convex Programs	p. 291
Adjoint Bifunctions and Dual Programs	p. 307
Fenchel's Duality Theorem	p. 327
The Maximum of a Convex Function	p. 342
Saddle-Functions	p. 349
Closures and Equivalence Classes	p. 359
Continuity and Differentiability of Saddle-functions	p. 370
Minimax Problems	p. 379
Conjugate Saddle-functions and Minimax Theorems	p. 388
The Algebra of Bifunctions	p. 401
Convex Processes	p. 413
Comments and References	p. 425
Bibliography	p. 433
Index	p. 447
Table of Contents provided by Blackwell. All Rights Reserved.

Convex Analysis

(PMS-28)

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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