Convex analysis and nonlinear optimization : theory and examples /

Convex analysis and nonlinear optimization : theory and examples /

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Bibliographic Details
Author / Creator:	Borwein, Jonathan M.
Imprint:	New York : Springer, c2000.
Description:	x, 273 p. ; 25 cm.
Language:	English
Series:	CMS books in mathematics ; 3
Subject:	Convex functions. Mathematical optimization. Nonlinear theories. Convex functions. Mathematical optimization. Nonlinear theories.
Format:	Print Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/4710972

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Other authors / contributors:	Lewis, Adrian S.
ISBN:	0387989404 (hardcover : alk. paper)
Notes:	Includes bibliographical references (p. 241-252) and index.

Table of Contents:

1. Background
1.1. Euclidean Spaces
1.2. Symmetric Matrices
2. Inequality Constraints
2.1. Optimality Conditions
2.2. Theorems of the Alternative
2.3. Max-functions
3. Fenchel Duality
3.1. Subgradients and Convex Functions
3.2. The Value Function
3.3. The Fenchel Conjugate
4. Convex Analysis
4.1. Continuity of Convex Functions
4.2. Fenchel Biconjugation
4.3. Lagrangian Duality
5. Special Cases
5.1. Polyhedral Convex Sets and Functions
5.2. Functions of Eigenvalues
5.3. Duality for Linear and Semidefinite Programming
5.4. Convex Process Duality
6. Nonsmooth Optimization
6.1. Generalized Derivatives
6.2. Regularity and Strict Differentiability
6.3. Tangent Cones
6.4. The Limiting Subdifferential
7. Karush-Kuhn-Tucker Theory
7.1. An Introduction to Metric Regularity
7.2. The Karush-Kuhn-Tucker Theorem
7.3. Metric Regularity and the Limiting Subdifferential
7.4. Second Order Conditions
8. Fixed Points
8.1. The Brouwer Fixed Point Theorem
8.2. Selection and the Kakutani-Fan Fixed Point Theorem
8.3. Variational Inequalities
9. Postscript: Infinite Versus Finite Dimensions
9.1. Introduction
9.2. Finite Dimensionality
9.3. Counterexamples and Exercises
9.4. Notes on Previous Chapters
10. List of Results and Notation
10.1. Named Results
10.2. Notation.