凸分析（英文版） [Convex Analysis] pdf epub mobi txt 电子书 下载 2025

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[德] 洛克菲拉 著

出版社： 世界图书出版公司

ISBN：9787510029608

版次：1

商品编码：10562623

包装：平装

外文名称：Convex Analysis

开本：24开

出版时间：2011-01-01

用纸：胶版纸

页数：451

正文语种：英文

内容简介

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.

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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. 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

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这个版本的书非常不错，便宜也够清晰

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经典教材，慢慢看！

评分☆☆☆☆☆

经典书籍，值得收藏

评分☆☆☆☆☆

非常好的经典书籍 一定要仔细看

评分☆☆☆☆☆

这是凸分析最古老也是最经典的教材，但对于刚刚接初优化的不太适合，要想啃下来，不过个五，六次估计是不行的，比较适合专业人员攻读。

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经典的一本书籍 很经典值得拥有经典的一本书籍 很经典值得拥有

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正在认真学习

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经典书籍，值得好好研读

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分析就是将研究对象的整体分为各个部分、方面、因素和层次，并分别地加以考察的认识活动。比如说，我们研究植物细胞，将它分为细胞壁，细胞膜、细胞质和细胞核几个不同部分来认识，并分别地考察各部分所特有的性质和功能，由此就可知，一个细胞外面包着一层透明的薄壁，这就是细胞壁，它有保护和支持作用；紧贴在细胞壁里面的一层很薄的膜，就是细胞膜，它控制着物质的出入，既不让有用的物质任意流出细胞，也不让有害的物质轻易地进入细胞，细胞膜里面包着的透明物质就是细胞质，细胞质里含有很多非常重要的物体，如植物绿色部分的细胞质里，含有制造有机养料的叶绿体，细胞质里还含有—个或几个象水泡似的液泡，细胞液含有糖分或带有酸味的物质；细胞质里还含有一个近似球形的细胞核，细胞核里含有在遗传上起着重大作用的物质。我们分别对植物细胞的各部分作如上的考察，这样的认识活动就是分析。