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

☆☆☆☆☆

[德] 洛剋菲拉 著

圖書標籤:

• 凸優化
• 凸分析
• 數學規劃
• 運籌學
• 優化理論
• 函數分析
• 非綫性規劃
• 應用數學
• 工業工程
• 理論基礎

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

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

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　　为了认识被研究对象的复杂构成，人们从不同的实践角度出发，提出所需要解决的问题，作出不同学科的理论分析。就以人们对水稻的认识来说吧，既有解剖学的分析，又有生理学的分析，还可以给予育种学、营养学、地理学等等方面的分析。各种分析的具体方式差别很大，然而，它们都离不开考察研究对象的组织成分，各种性能以及细部结构，只是侧重点不同而已。也就是说，任何分析都是由考察研究对象的“成分——性能——细都结构”诸环节构成的，但各以某—环节为主，其他环节为辅。

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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

评分☆☆☆☆☆

还不错，搞活动买的，价格合适

评分☆☆☆☆☆

　　为了认识被研究对象的复杂构成，人们从不同的实践角度出发，提出所需要解决的问题，作出不同学科的理论分析。就以人们对水稻的认识来说吧，既有解剖学的分析，又有生理学的分析，还可以给予育种学、营养学、地理学等等方面的分析。各种分析的具体方式差别很大，然而，它们都离不开考察研究对象的组织成分，各种性能以及细部结构，只是侧重点不同而已。也就是说，任何分析都是由考察研究对象的“成分——性能——细都结构”诸环节构成的，但各以某—环节为主，其他环节为辅。

评分☆☆☆☆☆

还不错的东东还可以还可以