The Resource Convex analysis, by R. Tyrrell Rockafellar
Convex analysis, by R. Tyrrell Rockafellar
 Summary
 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 saddlefunctions
 Language
 eng
 Extent
 1 online resource (xviii, 451 pages)
 Note
 "First published in the Princeton Mathematical Series in 1970"Title page verso
 Contents

 Cover; Title; Copright; Dedication; Preface; Contents; Introductory Remarks: a Guide for the Reader ; PART I: BASIC CONCEPTS; 1. Affine Sets; 2. Convex Sets and Cones ; 3. The Algebra of Convex Sets; 4. Convex Functions; 5. Functional Operations; PART II: TOPOLOGICAL PROPERTIES; 6. Relative Interiors of Convex Sets; 7. Closures of Convex Functions; 8. Recession Cones and Unboundedness; 9. Some Closedness Criteria; 10. Continuity of Convex Functions; PART III: DUALITY CORRESPONDENCES; 11. Separation Theorems; 12. Conjugates of Convex Functions; 13. Support Functions
 14. Polars of Convex Sets15. Polars of Convex Functions; 16. DualOperations; PART IV: REPRESENTATION AND INEQUALITIES; 17. Caratheodory's Theorem; 18. Extreme Points and Faces of Convex Sets; 19. Polyhedral Convex Sets and Functions; 20. Some Applications of Polyhedral Convexity; 21. Helly's Theorem and Systems of Inequalities; 22. Linear Inequalities; PART V: DIFFERENTIAL THEORY; 23. Directional Derivatives and Subgradients ; 24. Differential Continuity and Monotonicity.; 25. Differentiability of Convex Functions; 26. The Legendre Transformation
 PART VI: CONSTRAINED EXTREMUM PROBLEMS27. The Minimum of a Convex Function; 28. Ordinary Convex Programs and Lagrange Multipliers; 29. Bifunctions and Generalized Convex Programs; 30. Adjoint Bifunctions and Dual Programs; 31. Fenchel's Duality Theorem; 32. The Maximum of a Convex Function ; PART VII: SADDLEFUNCTIONS AND MINIMAX THEORY; 33. SaddleFunctions; 34. Closures and Equivalence Classes; 35. Continuity and Differentiability of Saddlefunctions; 36. Minimax Problems; 37. Conjugate Saddlefunctions and Minimax Theorems; PART VIII: CONVEX ALGEBRA
 38. The Algebra of Bifunctions39. Convex Processes; Comments and References ; Bibliography; Index
 Isbn
 9781400873173
 Label
 Convex analysis
 Title
 Convex analysis
 Statement of responsibility
 by R. Tyrrell Rockafellar
 Language
 eng
 Summary
 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 saddlefunctions
 Cataloging source
 N$T
 Index
 index present
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement

 Princeton landmarks in mathematics and physics
 Princeton paperbacks
 Label
 Convex analysis, by R. Tyrrell Rockafellar
 Note
 "First published in the Princeton Mathematical Series in 1970"Title page verso
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references (pages 433446) and index
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier.
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent.
 Contents

 Cover; Title; Copright; Dedication; Preface; Contents; Introductory Remarks: a Guide for the Reader ; PART I: BASIC CONCEPTS; 1. Affine Sets; 2. Convex Sets and Cones ; 3. The Algebra of Convex Sets; 4. Convex Functions; 5. Functional Operations; PART II: TOPOLOGICAL PROPERTIES; 6. Relative Interiors of Convex Sets; 7. Closures of Convex Functions; 8. Recession Cones and Unboundedness; 9. Some Closedness Criteria; 10. Continuity of Convex Functions; PART III: DUALITY CORRESPONDENCES; 11. Separation Theorems; 12. Conjugates of Convex Functions; 13. Support Functions
 14. Polars of Convex Sets15. Polars of Convex Functions; 16. DualOperations; PART IV: REPRESENTATION AND INEQUALITIES; 17. Caratheodory's Theorem; 18. Extreme Points and Faces of Convex Sets; 19. Polyhedral Convex Sets and Functions; 20. Some Applications of Polyhedral Convexity; 21. Helly's Theorem and Systems of Inequalities; 22. Linear Inequalities; PART V: DIFFERENTIAL THEORY; 23. Directional Derivatives and Subgradients ; 24. Differential Continuity and Monotonicity.; 25. Differentiability of Convex Functions; 26. The Legendre Transformation
 PART VI: CONSTRAINED EXTREMUM PROBLEMS27. The Minimum of a Convex Function; 28. Ordinary Convex Programs and Lagrange Multipliers; 29. Bifunctions and Generalized Convex Programs; 30. Adjoint Bifunctions and Dual Programs; 31. Fenchel's Duality Theorem; 32. The Maximum of a Convex Function ; PART VII: SADDLEFUNCTIONS AND MINIMAX THEORY; 33. SaddleFunctions; 34. Closures and Equivalence Classes; 35. Continuity and Differentiability of Saddlefunctions; 36. Minimax Problems; 37. Conjugate Saddlefunctions and Minimax Theorems; PART VIII: CONVEX ALGEBRA
 38. The Algebra of Bifunctions39. Convex Processes; Comments and References ; Bibliography; Index
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 http://library.link/vocab/discovery_link
 {'f': 'http://opac.lib.rpi.edu/record=b4319295'}
 Extent
 1 online resource (xviii, 451 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9781400873173
 Level of compression
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 Media category
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 Media MARC source
 rdamedia.
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