Fundamentals of Convex Analysis /

This book is an abridged version of the two volumes "Convex Analysis and Minimization Algorithms I and II" (Grundlehren der mathematischen Wissenschaften Vol. 305 and 306), which presented an introduction to the basic concepts in convex analysis and a study of convex minimization problems....

Full description

Bibliographic Details
Main Author: Hiriart-Urruty, Jean-Baptiste
Corporate Author: SpringerLink (Online service)
Other Authors: Lemaréchal, Claude
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2001.
Series:Grundlehren text editions.
Subjects:
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Introduction: Notation, Elementary Results
  • Convex Sets: Generalities; Convex Sets Attached to a Convex Set; Projection onto Closed Convex Sets; Separation and Applications; Conical Approximations of Convex Sets
  • Convex Functions: Basic Definitions and Examples; Functional Operations Preserving Convexity; Local and Global Behaviour of a Convex Function; First- and Second-Order Differentiation
  • Sublinearity and Support Functions: Sublinear Functions; The Support Function of a Nonempty Set; Correspondence Between Convex Sets and Sublinear Functions
  • Subdifferentials of Finite Convex Functions: The Subdifferential: Definitions and Interpretations; Local Properties of the Subdifferential; First Examples; Calculus Rules with Subdifferentials; Further Examples; The Subdifferential as a Multifunction
  • Conjugacy in Convex Analysis: The Convex Conjugate of a Function; Calculus Rules on the Conjugacy Operation; Various Examples; Differentiability of a Conjugate Function.