凸分析基礎（簡體書）

This book is an abridged version of our two-volume opus Convex Analysis and Minimization Algorithms [18], about which we have received very positive feedback from users, readers, lecturers ever since it was published-by Springer-Verlag in 1993. Its pedagogical qualities were particularly appreciated, in the combination with a rather advanced technical material.本書是《凸分析和極小化算法》(Convex Analysis and Minimization Algorithms I and II)的精簡本。原書介紹了凸分析中的基本概念和對凸極小化問題的研究。本書選出了兩卷書中的精華，刪除了一些被認為是艱深晦澀以及和數值分析雷同的內容。書中各章有大量習題。
目次：介紹：符號、基本結論；凸集；凸函數；次線性函數和支撐函數；有限凸函數的次微分；凸分析的共軛性。
讀者對象: 數學專業的研究生及數學工作者。

Preface
O. Introduction: Notation， Elementary Results
1 Some Facts About Lower and Upper Bounds
2 The Set of Extended Real Numbers
3 Linear and Bilinear Algebra
4 Differentiation in a Euclidean Space
5 Set-Valued Analysis
6 Recalls on Convex Functions of the Real Variable
Exercises
A. Convex Sets
1 Generalities
2 Convex Sets Attached to a Convex Set
3 Projection onto Closed Convex Sets
4 Separation and Applications
5 Conical Approximations of Convex Sets
Exercises
B. Convex Functions
1 Basic Definitions and Examples
2 Functional Operations Preserving Convexity
3 Local and Global Behaviour of a Convex Function
4 First-and Second-Order Differentiation
Preface
O. Introduction: Notation， Elementary Results
1 Some Facts About Lower and Upper Bounds
2 The Set of Extended Real Numbers
3 Linear and Bilinear Algebra
4 Differentiation in a Euclidean Space
5 Set-Valued Analysis
6 Recalls on Convex Functions of the Real Variable
Exercises
A. Convex Sets
1 Generalities
2 Convex Sets Attached to a Convex Set
3 Projection onto Closed Convex Sets
4 Separation and Applications
5 Conical Approximations of Convex Sets
Exercises
C. Sublinearity and Support Functions
1 Sublinear Functions
2 The Support Function of a Nonempty Set
3 Correspondence Between Convex Sets and Sublinear Functions
Exercises
D. Subdifferentials of Finite Convex Functions
1 The Subdifferential:Definitions and Interpretations
2 Local Properties of the Subdiffrential
3 First Examples
4 Calculus Rules with Subdifferentials
5 Further Examples
6 The Subdifferential as a Multifunction
Exercises
E. Conjugacy in Convex Analysis
1 The Convex Conjugate of a Function
2 Calculus Rules on the Conjugacy Operation
3 Various Examples
4 Differentiability of a Conjugate Function
Exercises
Bibliographical Comments
The Founding Fathers of the Discipline
References
Index