Primal and dual gap functions for generalized nash equilibrium problems and quasi-variational inequalities
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| Sprache: | English |
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2014
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Datensatz im Suchindex
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| adam_text | PRIMAL AND DUAL GAP FUNCTIONS
FOR GENERALIZED NASH EQUILIBRIUM PROBLEMS
AND QUASI-VARIATIONAL INEQUALITIES
DISSERTATION ZUR ERLANGUNG
DES NATURWISSENSCHAFTLICHEN DOKTORGRADES
DER JULIUS-MAXIMILIANS-UNIVERSITAT WIIRZBURG
VORGELEGT VON
NADJA HARMS
AUS
PROSTORNOJE
WIIRZBURG, 2014
EINGEREICHT AM: 16. JULI 2014
1. GUTACHTER: PROF. DR. CHRISTIAN KANZOW, UNIVERSITAT WIIRZBURG
2. GUTACHTER: PROF. DR. ANDREAS FISCHER, TECHNISCHE UNIVERSITAT DRESDEN
HTTP://D-NB.INFO/106668295X
CONTENTS
1. INTRODUCTION 1
2. PRELIMINARIES 3
2.1. TOOLS FROM VARIATIONAL ANALYSIS 3
2.2. A PIECEWISE SMOOTHNESS RESULT FOR A CONVEX PARAMETRIC NONLINEAR
PROGRAM . . 7
I. GENERALIZED NASH EQUILIBRIUM PROBLEMS 13
3. BACKGROUND ON GENERALIZED NASH EQUILIBRIUM PROBLEMS 15
3.1. DEFINITION AND OVERVIEW 15
3.2. REFORMULATIONS AS A CONSTRAINED OR UNCONSTRAINED OPTIMIZATION
PROBLEM .... 18
4. SMOOTHNESS PROPERTIES OF A PRIMAL GAP FUNCTION FOR GENERALIZED NASH
EQUI
LIBRIUM PROBLEMS 23
4.1. CONTINUITY PROPERTIES AND DOMAIN 23
4.2. DIFFERENTIABILITY PROPERTIES 30
5. SMOOTHNESS PROPERTIES OF A DUAL GAP FUNCTION FOR GENERALIZED NASH
EQUILIB
RIUM PROBLEMS 41
5.1. A SMOOTH DUAL GAP FUNCTION 41
5.2. SECOND-ORDER PROPERTIES 58
6. NUMERICAL RESULTS FOR GENERALIZED NASH EQUILIBRIUM PROBLEMS 61
6.1. PRIMAL GAP FUNCTION APPROACH 61
6.2. DUAL GAP FUNCTION APPROACH 64
6.3. COMPARING THE TWO APPROACHES 69
II. QUASI-VARIATIONAL INEQUALITIES 71
7. BACKGROUND ON QUASI-VARIATIONAL INEQUALITIES 73
7.1. DEFINITION AND OVERVIEW 73
7.2. PRELIMINARIES ON GAP FUNCTIONS 75
7.2.1. GAP FUNCTIONS FOR VARIATIONAL INEQUALITIES 75
7.2.2. GAP FUNCTIONS FOR QUASI-VARIATIONAL INEQUALITIES 76
V
CONTENTS
8. SPECIAL CLASSES OF QUASI-VARIATIONAL INEQUALITIES 81
8.1. QUASI-VARIATIONAL INEQUALITIES WITH GENERALIZED MOVING SETS 81
8.2. QUASI-VARIATIONAL INEQUALITIES WITH SET-VALUED MAPPINGS IN PRODUCT
FORM .... 86
8.3. APPLICATION TO GENERALIZED NASH EQUILIBRIUM PROBLEMS 88
9. SMOOTHNESS PROPERTIES OF A PRIMAL GAP FUNCTION FOR QUASI-VARIATIONAL
INEQUA
LITIES 91
9.1. CONTINUITY PROPERTIES AND DOMAIN 91
9.2. DIFFERENTIABILITY PROPERTIES 94
10. SMOOTHNESS PROPERTIES OF A DUAL GAP FUNCTION FOR QUASI-VARIATIONAL
INEQUALI
TIES 103
10.1. A SMOOTH DUAL GAP FUNCTION 103
10.2. SECOND-ORDER PROPERTIES 118
11. NUMERICAL RESULTS FOR QUASI-VARIATIONAL INEQUALITIES 123
11.1. PRIMAL GAP FUNCTION APPROACH
N
. ... 123
11.2. DUAL GAP FUNCTION APPROACH 126
FINAL REMARKS 129
BIBLIOGRAPHY 131
VI
|
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| author | Harms, Nadja |
| author_GND | (DE-588)1065838352 |
| author_facet | Harms, Nadja |
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| ctrlnum | (OCoLC)902826721 (DE-599)BVBBV042298335 |
| discipline | Mathematik |
| format | Thesis Book |
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| institution | BVB |
| language | English |
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| physical | IX, 140 S. Ill. |
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| spellingShingle | Harms, Nadja Primal and dual gap functions for generalized nash equilibrium problems and quasi-variational inequalities Parametrische Optimierung (DE-588)4044615-3 gnd Spieltheorie (DE-588)4056243-8 gnd Nash-Gleichgewicht (DE-588)4171190-7 gnd Dualitätstheorie (DE-588)4150801-4 gnd Nichtglatte Optimierung (DE-588)4120798-1 gnd |
| subject_GND | (DE-588)4044615-3 (DE-588)4056243-8 (DE-588)4171190-7 (DE-588)4150801-4 (DE-588)4120798-1 (DE-588)4113937-9 |
| title | Primal and dual gap functions for generalized nash equilibrium problems and quasi-variational inequalities |
| title_alt | Primale und duale Gap-Funktionen für verallgemeinerte Nash-Gleichgewichtsprobleme und Quasi-Variationsungleichungen |
| title_auth | Primal and dual gap functions for generalized nash equilibrium problems and quasi-variational inequalities |
| title_exact_search | Primal and dual gap functions for generalized nash equilibrium problems and quasi-variational inequalities |
| title_full | Primal and dual gap functions for generalized nash equilibrium problems and quasi-variational inequalities von Nadja Harms |
| title_fullStr | Primal and dual gap functions for generalized nash equilibrium problems and quasi-variational inequalities von Nadja Harms |
| title_full_unstemmed | Primal and dual gap functions for generalized nash equilibrium problems and quasi-variational inequalities von Nadja Harms |
| title_short | Primal and dual gap functions for generalized nash equilibrium problems and quasi-variational inequalities |
| title_sort | primal and dual gap functions for generalized nash equilibrium problems and quasi variational inequalities |
| topic | Parametrische Optimierung (DE-588)4044615-3 gnd Spieltheorie (DE-588)4056243-8 gnd Nash-Gleichgewicht (DE-588)4171190-7 gnd Dualitätstheorie (DE-588)4150801-4 gnd Nichtglatte Optimierung (DE-588)4120798-1 gnd |
| topic_facet | Parametrische Optimierung Spieltheorie Nash-Gleichgewicht Dualitätstheorie Nichtglatte Optimierung Hochschulschrift |
| url | https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-106027 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027735363&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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