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

世圖版兩種凸分析之一,研究的是凸分析與最優化理論

評分☆☆☆☆☆

可以的

評分☆☆☆☆☆

　　為什麼思維中要對客觀對象進行分析呢?我們知道，自然界中的任何事物都不是單純的和不可分的，而是具有復雜的構成。它們總是由不同的部分、方麵、因素和層次組成的。果核可以剖開，化閤物可以分解，所謂“元素”、“原子”和“基本粒子”也都不是單純的，都有其一定的結構。客觀事物構成的復雜性決定著思維分析的必要性。沒有分摺，人們對事物隻能有個渾沌的認識。

評分☆☆☆☆☆

書很好，慢慢看，我隻是為瞭點豆豆，還沒看

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☆☆☆☆☆

每次評價都要寫十個字

評分☆☆☆☆☆

凸分析的書。從中我們可以大緻瞭解到一些凸優化的概念，比如凸集，凸函數，凸優化問題，綫性規劃，二次規劃，二次約束二次規劃，半正定規劃等，從而對凸優化問題有個初步的認識。

評分☆☆☆☆☆

每次評價都要寫十個字

評分☆☆☆☆☆

經典書籍，值得好好研讀