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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 central role.
systems of inequalities， the minimum or maximum of a convex function over 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.

內頁插圖

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. Carath6odorys Theorem
18. Extreme Points and Faces of Convex Sets
19. Polyhedral Convex Sets and Functions
20. Some Applications of Polyhedral Convexity
21.Hellys 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. Fenchels 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

前言/序言

凸分析（英文版） [Convex Analysis] 下載 mobi epub pdf txt 電子書

評分☆☆☆☆☆

分析就是將研究對象的整體分為各個部分、方麵、因素和層次，並分彆地加以考察的認識活動。比如說，我們研究植物細胞，將它分為細胞壁，細胞膜、細胞質和細胞核幾個不同部分來認識，並分彆地考察各部分所特有的性質和功能，由此就可知，一個細胞外麵包著一層透明的薄壁，這就是細胞壁，它有保護和支持作用；緊貼在細胞壁裏麵的一層很薄的膜，就是細胞膜，它控製著物質的齣入，既不讓有用的物質任意流齣細胞，也不讓有害的物質輕易地進入細胞，細胞膜裏麵包著的透明物質就是細胞質，細胞質裏含有很多非常重要的物體，如植物綠色部分的細胞質裏，含有製造有機養料的葉綠體，細胞質裏還含有—個或幾個象水泡似的液泡，細胞液含有糖分或帶有酸味的物質；細胞質裏還含有一個近似球形的細胞核，細胞核裏含有在遺傳上起著重大作用的物質。我們分彆對植物細胞的各部分作如上的考察，這樣的認識活動就是分析。

評分☆☆☆☆☆

這個書可以說是“經典”瞭，因為一直是第一版，都齣瞭好多年瞭吧？

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正在學習ing

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管理學科的必讀書，考上博士用

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東西不錯 就是有點點貴，送貨很快

評分☆☆☆☆☆

大牛著作，純屬膜拜。

評分☆☆☆☆☆

既然本書價格不低，齣版社應該改多用點心思吧！裝訂和印刷相比我同單購買的《凸優化理論》差遠瞭！

評分☆☆☆☆☆

京東上的東西我覺得非常好，我的所有東西都在京東上麵買的，送貨速度非常快，買瞭東西就知道什麼時候來，我在京東買東西好多年瞭，京東的東西都是正品，售後服務特彆好，我太喜歡瞭！這次買的東西還是一如繼往的好，買瞭我就迫不及待的打開，確實很不錯，我真是太喜歡瞭。在京東消費很多，都成鑽石會員瞭，哈哈，以後還會買，所有的東西都在京東買，京東商城是生活首選！

評分☆☆☆☆☆

好書一本，值得購買，裏麵少許有筆誤。

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