Pub. Date:
Springer US
Nonsmooth Vector Functions and Continuous Optimization / Edition 1

Nonsmooth Vector Functions and Continuous Optimization / Edition 1

by V. Jeyakumar, Dinh The Luc


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Product Details

ISBN-13: 9780387737164
Publisher: Springer US
Publication date: 10/25/2007
Series: Springer Optimization and Its Applications , #10
Edition description: 2008
Pages: 270
Product dimensions: 6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

Preface     IX
Pseudo-Jacobian Matrices     1
Preliminaries     1
Pseudo-Jacobian Matrices     10
Nonsmooth Derivatives     14
Pseudo-Differentials and Pseudo-Hessians of Scalar Functions     23
Recession Matrices and Partial Pseudo-Jacobians     35
Constructing Stable Pseudo-Jacobians     40
Gateaux and Frechet Pseudo-Jacobians     49
Calculus Rules for Pseudo-Jacobians     57
Elementary Rules     57
The Mean Value Theorem and Taylor's Expansions     66
A General Chain Rule     82
Chain Rules Using Recession Pseudo-Jacobian Matrices     85
Chain Rules for Gateaux and Frechet Pseudo-Jacobians     93
Openness of Continuous Vector Functions     99
Equi-Invertibility and Equi-Surjectivity of Matrices     99
Open Mapping Theorems     110
Inverse and Implicit Function Theorems     115
Convex Interior Mapping Theorems     118
Metric Regularity and Pseudo-Lipschitzian Property     128
Nonsmooth Mathematical Programming Problems     143
First-Order Optimality Conditions     143
Second-Order Conditions     155
Composite Programming     168
Multiobjective Programming     186
Monotone Operators and Nonsmooth Variational Inequalities     207
Generalized Monotone Operators     207
Generalized Convex Functions     222
Variational Inequalities     230
Complementarity Problems     243
Bibliographical Notes     255
References     259
Notations     265
Index     267

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