Convex analysis / by R. Tyrrell Rockafellar.
Series Princeton mathematical series ; 28Editor: Princeton, N.J. : Princeton University Press, c1970Descripción: xviii, 451 p. ; 24 cmISBN: 0691080690Otra clasificación: 26.52 (46.00)Introductory Remarks: a Guide for the Reader xi PART I: BASIC CONCEPTS §1. Affine Sets [3] §2. Convex Sets and Cones [10] §3. The Algebra of Convex Sets [16] §4. Convex Functions [23] §5. Functional Operations [32] PART II: TOPOLOGICAL PROPERTIES §6. Relative Interiors of Convex Sets [43] §7. Closures of Convex Functions [51] §8. Recession Cones and Unboundedness [60] §9. Some Closedness Criteria [72] §10. Continuity of Convex Functions [82] PART III: DUALITY CORRESPONDENCES §11. Separation Theorems [95] §12. Conjugates of Convex Functions [102] §13. Support Functions [112] §14. Polars of Convex Sets [121] §15. Polars of Convex Functions [128] §16. Dual Operations [140] PART IV: REPRESENTATION AND INEQUALITIES §17. Caratheodory’s Theorem [153] §18. Extreme Points and Faces of Convex Sets [162] §19. Polyhedral Convex Sets and Functions [170] §20. Some Applications of Polyhedral Convexity [179] §21. Helly’s Theorem and Systems of Inequalities [185] §22. Linear Inequalities [198] PART V: DIFFERENTIAL THEORY §23. Directional Derivatives and Subgradients [213] §24. Differential Continuity and Monotonicity [227] §25. Differentiability of Convex Functions [241] §26. The Legendre Transformation [251] PART VI: CONSTRAINED EXTREMUM PROBLEMS §27. The Minimum of a Convex Function [263] §28. Ordinary Convex Programs and Lagrange Multipliers [273] §29. Bifunctions and Generalized Convex Programs [291] §30. Adjoint Bifunctions and Dual Programs [307] §31. Fenchel’s Duality Theorem [327] §32. The Maximum of a Convex Function [342] PART VII: SADDLE-FUNCTIONS AND MINIMAX THEORY §33. Saddle-Functions [349] §34. Closures and Equivalence Classes [359] §35. Continuity and Differentiability of Saddle-functions [370] §36. Minimax Problems [379] §37. Conjugate Saddle-functions and Minimax Theorems [388] PART VIII: CONVEX ALGEBRA §38. The Algebra of Bifunctions [401] §39. Convex Processes [413] Comments and References [425] Bibliography [433] Index [447]
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| 26 R487 Formas canónicas de aplicaciones diferenciales : | 26 R487 Formas canónicas de aplicaciones diferenciales : | 26 R495-2 Matemáticas técnicas / | 26 R682 Convex analysis / | 26 R682 Convex analysis / | 26 R888 Real analysis / | 26 R888-3 Real analysis / |
Bibliografía: p. 433-446.
Introductory Remarks: a Guide for the Reader xi --
PART I: BASIC CONCEPTS --
§1. Affine Sets [3] --
§2. Convex Sets and Cones [10] --
§3. The Algebra of Convex Sets [16] --
§4. Convex Functions [23] --
§5. Functional Operations [32] --
PART II: TOPOLOGICAL PROPERTIES --
§6. Relative Interiors of Convex Sets [43] --
§7. Closures of Convex Functions [51] --
§8. Recession Cones and Unboundedness [60] --
§9. Some Closedness Criteria [72] --
§10. Continuity of Convex Functions [82] --
PART III: DUALITY CORRESPONDENCES --
§11. Separation Theorems [95] --
§12. Conjugates of Convex Functions [102] --
§13. Support Functions [112] --
§14. Polars of Convex Sets [121] --
§15. Polars of Convex Functions [128] --
§16. Dual Operations [140] --
PART IV: REPRESENTATION AND INEQUALITIES --
§17. Caratheodory’s Theorem [153] --
§18. Extreme Points and Faces of Convex Sets [162] --
§19. Polyhedral Convex Sets and Functions [170] --
§20. Some Applications of Polyhedral Convexity [179] --
§21. Helly’s Theorem and Systems of Inequalities [185] --
§22. Linear Inequalities [198] --
PART V: DIFFERENTIAL THEORY --
§23. Directional Derivatives and Subgradients [213] --
§24. Differential Continuity and Monotonicity [227] --
§25. Differentiability of Convex Functions [241] --
§26. The Legendre Transformation [251] --
PART VI: CONSTRAINED EXTREMUM PROBLEMS --
§27. The Minimum of a Convex Function [263] --
§28. Ordinary Convex Programs and Lagrange Multipliers [273] --
§29. Bifunctions and Generalized Convex Programs [291] --
§30. Adjoint Bifunctions and Dual Programs [307] --
§31. Fenchel’s Duality Theorem [327] --
§32. The Maximum of a Convex Function [342] --
PART VII: SADDLE-FUNCTIONS AND MINIMAX THEORY --
§33. Saddle-Functions [349] --
§34. Closures and Equivalence Classes [359] --
§35. Continuity and Differentiability of Saddle-functions [370] --
§36. Minimax Problems [379] --
§37. Conjugate Saddle-functions and Minimax Theorems [388] --
PART VIII: CONVEX ALGEBRA --
§38. The Algebra of Bifunctions [401] --
§39. Convex Processes [413] --
Comments and References [425] --
Bibliography [433] --
Index [447] --
MR, 43 #445
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