凸分析

《凸分析》是2011年1月1日世界圖書出版公司出版的圖書，作者是洛克菲拉。

基本介紹

• 書名：凸分析
• 又名： Convex Analysis
• 作者：洛克菲拉（R.Tyrrell Rockafellar）
• ISBN：9787510029608
• 頁數：451頁
• 出版社：世界圖書出版公司
• 出版時間：2011年1月1日
• 裝幀：平裝
• 尺寸：22.2 x 14.8 x 2 cm
• 重量：581 g
• 開本：24
• 語種：英語

內容簡介

《凸分析(英文版)》內容簡介：Convexity has been increasingly important in recent years in the study of extremum problems in many areas of applied mathematics. The purpose of this book is to provide an exposition of the theory of convex sets and functions 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 among the topics treated, as well as basic results about the structure of convex sets and the continuity and differentiability of convex functions and saddle-functions. Duality is emphasized throughout, particularly in the form of Fenchers conjugacy correspondence for convex functions.

目錄

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