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....
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg :
Springer Berlin Heidelberg,
2001.
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| Series: | Grundlehren text editions.
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| 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.