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

簡體網頁||繁體網頁

☆☆☆☆☆

[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☆☆☆☆☆

每次評價都要寫十個字

評分☆☆☆☆☆

這是凸分析最古老也是最經典的教材，但對於剛剛接初優化的不太適閤，要想啃下來，不過個五，六次估計是不行的，比較適閤專業人員攻讀。

評分☆☆☆☆☆

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？

評分☆☆☆☆☆

好書一本，值得購買，裏麵少許有筆誤。

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☆☆☆☆☆

(* ?? ?* )?*

評分☆☆☆☆☆

書很經典，但是印刷質量感覺一般

評分☆☆☆☆☆