凸分析基礎(chǔ)

內(nèi)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.

書籍目錄

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

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