E-Book, Englisch, Band 10, 270 Seiten
Jeyakumar / Luc Nonsmooth Vector Functions and Continuous Optimization
1. Auflage 2007
ISBN: 978-0-387-73717-1
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, Band 10, 270 Seiten
Reihe: Springer Optimization and Its Applications
ISBN: 978-0-387-73717-1
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
Focusing on the study of nonsmooth vector functions, this book presents a comprehensive account of the calculus of generalized Jacobian matrices and their applications to continuous nonsmooth optimization problems, as well as variational inequalities in finite dimensions. The treatment is motivated by a desire to expose an elementary approach to nonsmooth calculus, using a set of matrices to replace the nonexistent Jacobian matrix of a continuous vector function.
Autoren/Hrsg.
Weitere Infos & Material
1;Contents;7
2;Preface;9
3;1 Pseudo-Jacobian Matrices;11
3.1;1.1 Preliminaries;11
3.2;1.2 Pseudo-Jacobian Matrices;20
3.3;1.3 Nonsmooth Derivatives;24
3.4;1.4 Pseudo-Differentials and Pseudo-Hessians of Scalar Functions;33
3.5;1.5 Recession Matrices and Partial Pseudo- Jacobians;45
3.6;1.6 Constructing Stable Pseudo-Jacobians;50
3.7;1.7 Gateaux and Frechet Pseudo-Jacobians;59
4;2 Calculus Rules for Pseudo- Jacobians;67
4.1;2.1 Elementary Rules;67
4.2;2.2 The Mean Value Theorem and Taylor’s Expansions;76
4.3;2.3 A General Chain Rule;92
4.4;2.4 Chain Rules Using Recession Pseudo- Jacobian Matrices;95
4.5;2.5 Chain Rules for Gateaux and Frechet Pseudo- Jacobians;103
5;3 Openness of Continuous Vector Functions;108
5.1;3.1 Equi-Invertibility and Equi-Surjectivity of Matrices;108
5.2;3.2 Open Mapping Theorems;119
5.3;3.3 Inverse and Implicit Function Theorems;124
5.4;3.4 Convex Interior Mapping Theorems;127
5.5;3.5 Metric Regularity and Pseudo-Lipschitzian Property;137
6;4 Nonsmooth Mathematical Programming Problems;152
6.1;4.1 First-Order Optimality Conditions ;152
6.2;4.2 Second-Order Conditions;164
6.3;4.3 Composite Programming ;177
6.4;4.4 Multiobjective Programming ;195
7;5 Monotone Operators and Nonsmooth Variational Inequalities;216
7.1;5.1 Generalized Monotone Operators;216
7.2;5.2 Generalized Convex Functions;231
7.3;5.3 Variational Inequalities;239
7.4;5.4 Complementarity Problems;252
8;Bibliographical Notes;264
9;References;268
10;Notations;274
11;Index;275
