凸分析（英文版） [Convex Analysis] pdf epub mobi txt 電子書 下載 2025

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[德] 洛剋菲拉 著

齣版社： 世界圖書齣版公司

ISBN：9787510029608

版次：1

商品編碼：10562623

包裝：平裝

外文名稱：Convex Analysis

開本：24開

齣版時間：2011-01-01

用紙：膠版紙

頁數：451

正文語種：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

評分☆☆☆☆☆

書很好，速度也很快，專業書籍值得一閱

評分☆☆☆☆☆

內容不錯，就是紙張太差

評分☆☆☆☆☆

經典書籍，值得好好研讀

評分☆☆☆☆☆

世圖北京公司!

評分☆☆☆☆☆

想說說書的裝訂和印刷問題。拿到的書最後幾頁竟然有很多小孔，難道是被蟲蛀瞭？

評分☆☆☆☆☆

　　為瞭認識被研究對象的復雜構成，人們從不同的實踐角度齣發，提齣所需要解決的問題，作齣不同學科的理論分析。就以人們對水稻的認識來說吧，既有解剖學的分析，又有生理學的分析，還可以給予育種學、營養學、地理學等等方麵的分析。各種分析的具體方式差彆很大，然而，它們都離不開考察研究對象的組織成分，各種性能以及細部結構，隻是側重點不同而已。也就是說，任何分析都是由考察研究對象的“成分——性能——細都結構”諸環節構成的，但各以某—環節為主，其他環節為輔。

評分☆☆☆☆☆

大牛著作，純屬膜拜。

評分☆☆☆☆☆

英文原版，比翻譯過來的中文版要好的多，雖然看起來有難度，但是有助於研究！

評分☆☆☆☆☆

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