Convex analysis
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| Sprache: | English |
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Princeton, N.J.
Princeton University Press
1997, ©1970
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| Schriftenreihe: | Princeton landmarks in mathematics and physics
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| 100 | 1 | |a Rockafellar, R. Tyrrell |d 1935- |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Convex analysis |c by R. Tyrrell Rockafellar |
| 264 | 1 | |a Princeton, N.J. |b Princeton University Press |c 1997, ©1970 | |
| 300 | |a 1 online resource (xviii, 451 pages) | ||
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| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 38. The Algebra of Bifunctions39. Convex Processes; Comments and References ; Bibliography; Index | |
| 505 | 8 | |a 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 | |
| 650 | 7 | |a Convex domains |2 fast | |
| 650 | 7 | |a Convex functions |2 fast | |
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| 650 | 7 | |a MATHEMATICS / Mathematical Analysis |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS / Optimization |2 bisacsh | |
| 650 | 4 | |a Convex domains | |
| 650 | 4 | |a Mathematical analysis | |
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Convex domains | |
| 650 | 4 | |a Convex functions | |
| 650 | 4 | |a Mathematical analysis | |
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Datensatz im Suchindex
| _version_ | 1804175382683844608 |
|---|---|
| any_adam_object | |
| author | Rockafellar, R. Tyrrell 1935- |
| author_facet | Rockafellar, R. Tyrrell 1935- |
| author_role | aut |
| author_sort | Rockafellar, R. Tyrrell 1935- |
| author_variant | r t r rt rtr |
| building | Verbundindex |
| bvnumber | BV043028177 |
| collection | ZDB-4-EBA |
| 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: 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 38. The Algebra of Bifunctions39. Convex Processes; Comments and References ; Bibliography; Index 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 |
| ctrlnum | (OCoLC)905969889 (DE-599)BVBBV043028177 |
| dewey-full | 515.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.64 |
| dewey-search | 515.64 |
| dewey-sort | 3515.64 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043028177 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:15:24Z |
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| series2 | Princeton landmarks in mathematics and physics |
| spelling | Rockafellar, R. Tyrrell 1935- Verfasser aut Convex analysis by R. Tyrrell Rockafellar Princeton, N.J. Princeton University Press 1997, ©1970 1 online resource (xviii, 451 pages) txt rdacontent c rdamedia cr rdacarrier Princeton landmarks in mathematics and physics "First published in the Princeton Mathematical Series in 1970"--Title page verso Print version record 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: 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 38. The Algebra of Bifunctions39. Convex Processes; Comments and References ; Bibliography; Index 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 Convex domains fast Convex functions fast Mathematical analysis fast Konvexe Analysis swd MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh MATHEMATICS / Optimization bisacsh Convex domains Mathematical analysis Mathematics Mathematik Convex functions Konvexität (DE-588)4114284-6 gnd rswk-swf Konvexe Analysis (DE-588)4138566-4 gnd rswk-swf Konvexe Analysis (DE-588)4138566-4 s 1\p DE-604 Konvexität (DE-588)4114284-6 s 2\p DE-604 Erscheint auch als Druck-Ausgabe Rockafellar, R Tyrrell, 1935-. Convex analysis http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=969057 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rockafellar, R. Tyrrell 1935- Convex analysis 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: 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 38. The Algebra of Bifunctions39. Convex Processes; Comments and References ; Bibliography; Index 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 Convex domains fast Convex functions fast Mathematical analysis fast Konvexe Analysis swd MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh MATHEMATICS / Optimization bisacsh Convex domains Mathematical analysis Mathematics Mathematik Convex functions Konvexität (DE-588)4114284-6 gnd Konvexe Analysis (DE-588)4138566-4 gnd |
| subject_GND | (DE-588)4114284-6 (DE-588)4138566-4 |
| title | Convex analysis |
| title_auth | Convex analysis |
| title_exact_search | Convex analysis |
| title_full | Convex analysis by R. Tyrrell Rockafellar |
| title_fullStr | Convex analysis by R. Tyrrell Rockafellar |
| title_full_unstemmed | Convex analysis by R. Tyrrell Rockafellar |
| title_short | Convex analysis |
| title_sort | convex analysis |
| topic | Convex domains fast Convex functions fast Mathematical analysis fast Konvexe Analysis swd MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh MATHEMATICS / Optimization bisacsh Convex domains Mathematical analysis Mathematics Mathematik Convex functions Konvexität (DE-588)4114284-6 gnd Konvexe Analysis (DE-588)4138566-4 gnd |
| topic_facet | Convex domains Convex functions Mathematical analysis Konvexe Analysis MATHEMATICS / Calculus MATHEMATICS / Mathematical Analysis MATHEMATICS / Optimization Mathematics Mathematik Konvexität |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=969057 |
| work_keys_str_mv | AT rockafellarrtyrrell convexanalysis |