| 词条 | 凸分析 |
| 释义 | 图书信息出版社: 世界图书出版公司; 第1版 (2011年1月1日) 外文书名: Convex Analysis 平装: 451页 正文语种: 英语 开本: 24 ISBN: 9787510029608, 7510029600 条形码: 9787510029608 尺寸: 22.2 x 14.8 x 2 cm 重量: 581 g 作者简介作者：（德国）洛克菲拉（R.Tyrrell Rockafellar） 内容简介《凸分析(英文版)》内容简介：Convexity has been increasingly important in recent years in the studyof extremum problems in many areas of applied mathematics. The purposeof this book is to provide an exposition of the theory of convex sets andfunctions in which applications to extremum problems play the centralrole. Systems of inequalities, the minimum or maximum of a convex functionover a convex set, Lagrange multipliers, and minimax theorems are amongthe topics treated, as well as basic results about the structure of convexsets and the continuity and differentiability of convex functions and saddle-functions. Duality is emphasized throughout, particularly in the form ofFenchers conjugacy correspondence for convex functions. 目录Preface . Introductory Remarks: a Guide for the Reader PART l: 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 Sels 7. Closures of Convex Functions 8. Recession Cones and Unboundedness 9. Some CIosedness Criteria 10. Continuity of Convex Functions PART Ⅲ: DUALITY CORRESPONDENCES 11. Separation Theorems 12. Conjugates of Convex Functions 13. Support Furctions 14. Polars of Convex Sets 15. Polars of Convex Functions 16.Dual Operations PART IV: REPRESENTATION AND INEQUALITIES 17. Carath6odory'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 CONTENTS 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 PROBLEMS 27. 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 Bifunctions 39. Convex Processes . Comments and References Bibliography Index |
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