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Duality in Optimization and Variational Inequalities : Optimization Theory and Applications - C. J. Goh

Duality in Optimization and Variational Inequalities

Optimization Theory and Applications

Hardcover Published: 1st May 2002
ISBN: 9780415274791
Number Of Pages: 336

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Although presented as a topic of low emphasis in introductory course work, duality plays a central role in optimization theory and application. This comprehensive volume covers a wide range of duality topics ranging from simple ideas in network flows to complex issues in non-convex optimization and multicriteria problems. In addition, it examines duality in the context of variational inequalities and vector variational inequalities, as generalizations to optimization. Duality in Optimization and Variational Inequalities is intended for researchers and practitioners of optimization with the aim of enhancing their understanding of duality and offers a wider appreciation of optimality conditions in various scenarios and under different assumptions. It will enable the reader to use duality to devise more effective computational methods, and to aid more meaningful interpretation of optimization and variational inequality problems.

Mathematical Preliminaries
Basic Notations and a List of Symbols
Elements of Convex Analysis in Euclidean Spaces
Fenchel Transform and Conjugate Duality
Elements of Graph Theory
Elements of Optimization and Variational Inequalities
Weak/Strong Duality, Duality Gap and Gap Function
Motivations for Studying Duality
Duality in Network Optimization
Duality of Paths and Cuts and Minimum Spanning Trees
Duality in a Painted Network
Flow, Divergence, Potential and Differential
Duality of Max Flow Min Cut
Duality of Max Match Min Block
Duality of Max Tension Min Path
Duality of Feasible Flow and Feasible Potential
Duality of Linear Optimal Flow and Optimal Potential
Duality of Convex Optimal Flow and Optimal Potential
Duality in Linear Systems
A Crash Course in Linear Programming
Duality in Linear Programming
Duality and Complementary Slackness
Duality and Theorems of Alternatives
Painted Index Theory
Duality in Monotropic Optimization
Duality in Convex Nonlinear Systems
Conjugate Duality in Unconstrained Optimization
Optimality Conditions for Constrained Optimization
Lagrangian Duality
Lagrangian Duality Specialized to LP, QP and MP
Wolfe Duality and Gap Functions for Convex Optimization
Duality in Nonconvex Systems
Examples of NonZero Duality Gaps
Zero Duality Gap Via a Nonlinear Lagrangian Function
Optimality Conditions Via a Monotone Function
Optimality Condtions Via a Monotone Composition Formulation
Zero Duality Gap Via an Alternate Lagrangian Function
Zero Duality Gap fpr a Discrete Optimization Problem
Zero Duality Gap Via an Extended Lagrangian Function
Duality in Variational Inequalities
Duality in Variational Inequalities
Gap Functions for Variational Inequalities
Primal and Dual Gap Functions for Extended Variational Inequalities
Gap Functions and Dual Fenchel Optimization
Elements of Multicriteria Optimization
Elements of Multicriteria Convex Analysis
Vector Conjugate Duality
Scalarization of Multicriteria Optimization
Optimality Conditions for Multicriteria Optimization
Duality in Multicriteria Optimization
Duality in Linear Multicriteria Optimization
Conjugate Duality in Convex Multicriteria Optimization
Lagrangian Duality in Convex Multicriteria Optimization
A Case of Symmetric and Self Duality
Gap Functions for Convex Multicriteria Optimization
Duality in Convex Composite Multicriteria Optimization
Duality in Vector Variational Inequalities
Introductions to Vector Variational Inequalities
Scalarization of Vector Variational Inequalities
Duality in Extended Vector Variational Inequalities
Gap Functions for Extended Vector Variational Inequalities
Generalized Gap Functions
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780415274791
ISBN-10: 0415274796
Series: Optimization Theory and Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 336
Published: 1st May 2002
Country of Publication: GB
Dimensions (cm): 25.71 x 17.37  x 2.34
Weight (kg): 0.73
Edition Number: 1