| Description |
1 online resource (xviii, 451 pages). |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
Princeton landmarks in mathematics and physics
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Princeton paperbacks
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Princeton landmarks in mathematics and physics.
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Princeton paperbacks.
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| Note |
"First published in the Princeton Mathematical Series in 1970"--Title page verso. |
| Bibliography |
Includes bibliographical references (pages 433-446) and index. |
| 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 |
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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 |
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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: SADDLE-FUNCTIONS AND MINIMAX THEORY; 33. Saddle-Functions; 34. Closures and Equivalence Classes; 35. Continuity and Differentiability of Saddle-functions; 36. Minimax Problems; 37. Conjugate Saddle-functions and Minimax Theorems; PART VIII: CONVEX ALGEBRA |
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38. The Algebra of Bifunctions39. Convex Processes; Comments and References ; Bibliography; Index |
| 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 saddle-functions. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Convex domains.
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Convex domains. |
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Convex functions.
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Convex functions. |
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Mathematical analysis.
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Mathematical analysis. |
| Genre/Form |
Electronic books.
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Electronic books.
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| Other Form: |
Print version: Rockafellar, R. Tyrrell, 1935- Convex analysis. Princeton, N.J. : Princeton University Press, 1997, ©1970 0691080690 (OCoLC)37202405 |
| ISBN |
9781400873173 electronic book |
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1400873177 electronic book |
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0691080690 |
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9780691080697 |
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0691015864 |
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9780691015866 |
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