Combined relaxation methods for variational inequalities:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London
Springer
2001
|
| Series: | Lecture notes in economics and mathematical systems
495 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 181 S. |
| ISBN: | 3540679995 |
Staff View
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| 100 | 1 | |a Konnov, Igor V. |d 1958- |e Verfasser |0 (DE-588)12224740X |4 aut | |
| 245 | 1 | 0 | |a Combined relaxation methods for variational inequalities |c Igor Konnov |
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Record in the Search Index
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| adam_text | Table of Contents
Notation and Convention 1
1. Variational Inequalities with Continuous Mappings 3
1.1 Problem Formulation and Basic Facts 3
1.1.1 Existence and Uniqueness Results 3
1.1.2 Variational Inequalities and Related Problems 8
1.2 Main Idea of CR Methods 15
1.2.1 Newton like Iterations 15
1.2.2 Basic Properties of CR Methods 19
1.3 Implementable CR Methods 24
1.3.1 A CR Method and its Properties 24
1.3.2 Convergence and Rates of Convergence 26
1.3.3 A Modified Line Search 32
1.3.4 Acceleration Techniques for CR Methods 35
1.4 Modified Rules for Computing Iteration Parameters 38
1.4.1 A Modified Rule for Computing the Stepsize 38
1.4.2 A Modified Rule for Computing the Descent Direction 42
1.5 CR Method Based on a Frank Wolfe Type Auxiliary
Procedure 47
1.5.1 Description of the Method 47
1.5.2 Convergence 48
1.6 CR Method for Variational Inequalities with
Nonlinear Constraints 50
1.6.1 A Modified Basic Scheme for CR Methods 50
1.6.2 Description of the Method 51
1.6.3 Convergence 53
2. Variational Inequalities with Multivalued Mappings 57
2.1 Problem Formulation and Basic Facts 57
2.1.1 Existence and Uniqueness Results 57
2.1.2 Generalized Variational Inequalities and
Related Problems 60
2.1.3 Equilibrium and Mixed Variational Inequality
Problems 65
X Table of Contents
2.2 CR Method for the Mixed Variational Inequality Problem ... 72
2.2.1 Description of the Method 72
2.2.2 Convergence 74
2.2.3 Rate of Convergence 77
2.3 CR Method for the Generalized Variational Inequality
Problem 80
2.3.1 Description of the Method 80
2.3.2 Properties of Auxiliary Mappings 82
2.3.3 Convergence 83
2.3.4 Complexity Estimates 85
2.3.5 Modifications 92
2.4 CR Method for Multivalued Inclusions 95
2.4.1 An Inexact CR Method for Multivalued Inclusions .... 95
2.4.2 Convergence 97
2.5 Decomposable CR Method 101
2.5.1 Properties of Auxiliary Mappings 102
2.5.2 Description of the Method 104
2.5.3 Convergence 106
3. Applications and Numerical Experiments 109
3.1 Iterative Methods for Non Strictly Monotone Variational
Inequalities 109
3.1.1 The Proximal Point Method 109
3.1.2 Regularization and Averaging Methods 112
3.1.3 The Ellipsoid Method 114
3.1.4 The Extragradient Method 116
3.2 Economic Equilibrium Problems 118
3.2.1 Economic Equilibrium Models as Complementarity
Problems 118
3.2.2 Economic Equilibrium Models with Monotone
Mappings 119
3.2.3 The Linear Exchange Model 121
3.2.4 The General Equilibrium Model 126
3.2.5 The Oligopolistic Equilibrium Model 128
3.3 Numerical Experiments with Test Problems 133
3.3.1 Systems of Linear Equations 133
3.3.2 Linear Complementarity Problems 134
3.3.3 Linear Variational Inequalities 136
3.3.4 Nonlinear Complementarity Problems 138
3.3.5 Nonlinear Variational Inequalities 140
4. Auxiliary Results 143
4.1 Feasible Quasi Nonexpansive Mappings 143
4.1.1 Exterior Point Algorithms 143
4.1.2 Feasible Point Algorithms 145
Table of Contents XI
4.2 Error Bounds for Linearly Constrained Problems 150
4.2.1 Preliminaries 150
4.2.2 Error Bounds 152
4.3 A Relaxation Subgradient Method Without Linesearch 154
4.3.1 Description of the Method 154
4.3.2 Convergence 155
4.3.3 Rate of Convergence 159
Bibliographical Notes 161
References 167
Index 179
|
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| indexdate | 2024-07-09T18:43:39Z |
| institution | BVB |
| isbn | 3540679995 |
| language | English |
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| physical | XI, 181 S. |
| publishDate | 2001 |
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| series | Lecture notes in economics and mathematical systems |
| series2 | Lecture notes in economics and mathematical systems |
| spelling | Konnov, Igor V. 1958- Verfasser (DE-588)12224740X aut Combined relaxation methods for variational inequalities Igor Konnov Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London Springer 2001 XI, 181 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in economics and mathematical systems 495 Convergentie (wiskunde) gtt Inégalités variationnelles Inégalités variationnelles ram Oplossingen (wiskunde) gtt Relaxatie gtt Relaxation, Méthodes de (Mathématiques) Relaxation, Méthodes de (mathématiques) ram Variatieongelijkheden gtt Relaxation methods (Mathematics) Variational inequalities (Mathematics) Relaxationsmethode (DE-588)4451085-8 gnd rswk-swf Variationsungleichung (DE-588)4187420-1 gnd rswk-swf Variationsungleichung (DE-588)4187420-1 s Relaxationsmethode (DE-588)4451085-8 s DE-604 Lecture notes in economics and mathematical systems 495 (DE-604)BV000000036 495 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009079542&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Konnov, Igor V. 1958- Combined relaxation methods for variational inequalities Lecture notes in economics and mathematical systems Convergentie (wiskunde) gtt Inégalités variationnelles Inégalités variationnelles ram Oplossingen (wiskunde) gtt Relaxatie gtt Relaxation, Méthodes de (Mathématiques) Relaxation, Méthodes de (mathématiques) ram Variatieongelijkheden gtt Relaxation methods (Mathematics) Variational inequalities (Mathematics) Relaxationsmethode (DE-588)4451085-8 gnd Variationsungleichung (DE-588)4187420-1 gnd |
| subject_GND | (DE-588)4451085-8 (DE-588)4187420-1 |
| title | Combined relaxation methods for variational inequalities |
| title_auth | Combined relaxation methods for variational inequalities |
| title_exact_search | Combined relaxation methods for variational inequalities |
| title_full | Combined relaxation methods for variational inequalities Igor Konnov |
| title_fullStr | Combined relaxation methods for variational inequalities Igor Konnov |
| title_full_unstemmed | Combined relaxation methods for variational inequalities Igor Konnov |
| title_short | Combined relaxation methods for variational inequalities |
| title_sort | combined relaxation methods for variational inequalities |
| topic | Convergentie (wiskunde) gtt Inégalités variationnelles Inégalités variationnelles ram Oplossingen (wiskunde) gtt Relaxatie gtt Relaxation, Méthodes de (Mathématiques) Relaxation, Méthodes de (mathématiques) ram Variatieongelijkheden gtt Relaxation methods (Mathematics) Variational inequalities (Mathematics) Relaxationsmethode (DE-588)4451085-8 gnd Variationsungleichung (DE-588)4187420-1 gnd |
| topic_facet | Convergentie (wiskunde) Inégalités variationnelles Oplossingen (wiskunde) Relaxatie Relaxation, Méthodes de (Mathématiques) Relaxation, Méthodes de (mathématiques) Variatieongelijkheden Relaxation methods (Mathematics) Variational inequalities (Mathematics) Relaxationsmethode Variationsungleichung |
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