Convex Analysis (pms-28)

Name: Convex Analysis (pms-28)
Price: 61.04 USD
Availability: InStock
ISBN: 9780691015866

ISBN-10: 0691015864

ISBN-13: 9780691015866

Edition: 1970

Authors: Ralph Tyrell Rockafellar

List price: $115.00

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Description:

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…

Book details

List price: $115.00
Copyright year: 1970
Publisher: Princeton University Press
Publication date: 1/12/1997
Binding: Paperback
Pages: 472
Size: 5.98" wide x 9.02" long x 0.98" tall
Weight: 1.738
Language: English



Preface


Introductory Remarks: A Guide for the Reader



Affine Sets



Convex Sets and Cones



The Algebra of Convex Sets



Convex Functions



Functional Operations



Relative Interiors of Convex Sets



Closures of Convex Functions



Recession Cones and Unboundedness



Some Closedness Criteria



Continuity of Convex Functions



Separation Theorems



Conjugates of Convex Functions



Support Functions



Polars of Convex Sets



Polars of Convex Functions



Dual Operations



Caratheodory's Theorem



Extreme Points and Faces of Convex Sets



Polyhedral Convex Sets and Functions



Some Applications of Polyhedral Convexity



Helly's Theorem and Systems of Inequalities



Linear Inequalities



Directional Derivatives and Subgradients



Differential Continuity and Monotonicity



Differentiability of Convex Functions



The Legendre Transformation



The Minimum of a Convex Function



Ordinary Convex Programs and Lagrange Multipliers



Bifunctions and Generalized Convex Programs



Adjoint Bifunctions and Dual Programs



Fenchel's Duality Theorem



The Maximum of a Convex Function



Saddle-Functions



Closures and Equivalence Classes



Continuity and Differentiability of Saddle-functions



Minimax Problems



Conjugate Saddle-functions and Minimax Theorems



The Algebra of Bifunctions



Convex Processes


Comments and References


Bibliography


Index