凸分析基础

出版时间：2004-4  出版社：世界图书出版公司  作者：Jean-Baptiste  页数：259  
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内容概要

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.

书籍目录

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 DifferentiationPreface 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  ExercisesD. 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  ExercisesE. 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  ExercisesBibliographical CommentsThe Founding Fathers of the DisciplineReferencesIndex

用户评论 (总计12条)

•   对于凸分析的学者，必不可少，相对国内的书籍，挺好的一本书
•   凸分析,很好的书，值得学习
•   书的质量还不错，内容待评价
•   买来收藏,不错的金融工程用书买来收藏,不错的金融工程用书买来收藏,不错的金融工程用书
•   顶级的原著教材，质量也很不错！！
•   专业要用 很好
•   很喜欢的书，真的不错，推荐购买。
•   还不错的一本入门书。对变分法的基础知识掌握不够的话，这本书是可以起到详细补充和深刻理解的作用
•   刚拿到书，看看再说
•   这本书还是不错，直接看英文能了解的更直观些
•   内容不错，不过纸质量不太满意
•   书的内容是没有问题的，袁亚湘院士上凸分析课的教材，问题在于当当给我的书显得很旧，书角有很多褶皱，纸张也不好，字体太小，看起来不舒服