Computing equilibria and fixed points: the solution of nonlinear inequalities
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Kluwer
1999
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| Schriftenreihe: | [Theory and decision library / C]
21 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 341 S. graph. Darst. |
| ISBN: | 0792383958 |
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| 245 | 1 | 0 | |a Computing equilibria and fixed points |b the solution of nonlinear inequalities |c by Zaifu Yang |
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| 650 | 7 | |a Speltheorie |2 gtt | |
| 650 | 4 | |a Fixed point theory | |
| 650 | 4 | |a Game theory | |
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Datensatz im Suchindex
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| adam_text | IMAGE 1
COMPUTING EQUILIBRIA AND
FIXED POINTS
THE SOLUTION OF NONLINEAR INEQUALITIES
BY
ZAIFU YANG
YOKOHAMA NATIONAL UNIVERSITY, JAPAN
KLUWER ACADEMIC PUBLISHERS BOSTON/ DORDRECHT/ LONDON
IMAGE 2
TABLE OF CONTENTS
PREFACE V
1 MATHEMATICAL PRELIMINARIES 1
1.1 INTRODUCTION 1
1.2 BASIC NOTATION AND TERMINOLOGY 1
1.3 BASIC POLYHEDRAL THEORY 5
1.4 SIMPLICES, TRIANGULATIONS AND GRAPHS 8
1.5 BROUWER S THEOREM AND SPERNER S LEMMA 17
1.6 KAKUTANI S THEOREM AND BROWDER S THEOREM 25
1.7 THEOREMS OF TARSKI, CARISTI AND EKELAND 31
2 APPLICATIONS IN GAME THEORY AND ECONOMICS 37
2.1 INTRODUCTION 37
2.2 THE CORE OF A GAME 37
2.3 NASH, PERFECT NASH, AND PROPER NASH EQUILIBRIA 40
2.4 A PURE EXCHANGE ECONOMY 43
2.5 AN EXCHANGE ECONOMY WITH PRICE RIGIDITIES 46
2.6 AN EXCHANGE ECONOMY WITH LINEAR TECHNOLOGIES 51
2.7 AN EXCHANGE ECONOMY WITH NON-CONVEX TECHNOLOGIES 53
2.8 AN EXCHANGE ECONOMY WITH INDIVISIBILITIES 55
2.9 AN EXCHANGE ECONOMY UNDER UNCERTAINTY 57
3 FIRST ALGORITHMS FOR APPROXIMATING FIXED POINTS 61
3.1 INTRODUCTION 61
3.2 INTEGER LABELING AND APPROXIMATION 61
3.3 SCARF S ALGORITHM 65
3.4 KUHN S ARTIFICIAL START ALGORITHM 71
3.5 KUHN S VARIABLE DIMENSION ALGORITHM 74
3.6 CONCLUDING REMARKS 77
4 SIMPLICIAL HOMOTOPY ALGORITHMS 79
4.1 INTRODUCTION J . 79
4.2 VECTOR LABELING AND LEXICOGRAPHIC SYSTEM 80
4.3 MERRILPS ALGORITHM 84
4.4 EAVES ALGORITHM ON S N X [L,OO) 90
4.5 EAVES-SAIGAL S ALGORITHM ON R N X [L,OO) 96
I
IMAGE 3
II TABLE OF CONTENTS
5 VARIABLE DIMENSION RESTART ALGORITHMS 101
5.1 INTRODUCTION 101
5.2 VAN DER LAAN-TALMAN S ALGORITHM O N 5 N 101
5.3 VAN DER LAAN-TALMAN S ALGORITHM ON R N 105
5.4 CONCLUDING REMARKS 112
6 AN ALGORITHM FOR INTEGER LINEAR PROGRAMMING 115
6.1 INTRODUCTION 115
6.2 THE PROBLEM: AN NP-COMPLETE PROBLEM 116
6.3 THE INTEGER LABELING ALGORITHM 120
6.4 UNIMODULAR TRANSFORMATION 134
6.5 NUMERICAL RESULTS 142
7 REFINEMENT AND STABILITY OF STATIONARY POINTS 147
7.1 INTRODUCTION 147
7.2 THE CONCEPT OF ROBUST STATIONARY POINT 149
7.3 THE P-TRIANGULATION OF THE UNIT SIMPLEX 150
7.4 THE ADAPTIVE SIMPLICIAL ALGORITHM . . . . 154
7.5 EXAMPLES AND RESOLUTION OF DEGENERACY 162
7.6 EXTENSION TO GENERAL POLYTOPES 167
8 COMPUTING A CONTINUUM OF ZERO POINTS 171
8.1 INTRODUCTION 171
8.2 A GENERAL PROBLEM AND AN ECONOMIC MODEL 173
8.3 AN ALGORITHM FOR COMPUTING A CONTINUUM OF ZERO POINTS . .. 174 8.4
EXISTENCE OF A CONTINUUM OF ZERO POINTS 183
8.5 AN ILLUSTRATION OF THE ALGORITHM 187
8.6 A CONSTRUCTIVE PROOF FOR BROWDER S THEOREM 191
9 COMPUTING STATIONARY POINTS ON POLYTOPES 195
9.1 INTRODUCTION 195
9.2 BASIC THEOREMS FOR RESOLVING DEGENERACY 196
9.3 AN ALGORITHM FOR FINDING ZERO POINTS 204
9.4 AN ALGORITHM FOR FINDING STATIONARY POINTS 210
9.5 THE V-TRIANGULATION OF POLYTOPES 214
10 THE COMPUTATION OF ANTIPODAL FIXED POINTS 217
10.1 INTRODUCTION 217
10.2 BORSUK-ULAM S THEOREM AND TUCKER S THEOREM 217
10.3 THE AS-TRIANGULATION OF C N 221
10.4 THE INTEGER LABELING REFLECTION ALGORITHM 225
10.5 THE VECTOR LABELING REFLECTION ALGORITHM 229
IMAGE 4
TABLE OF CONTENTS III
11 COMPUTING ALL ROOTS OF UNIVARIATE POLYNOTNIALS 230
11.1 INTRODUCTION 239
11.2 AN INTEGER LABELING RULE 240
11.3 A TRIANGULATION OF C X [-L,OO) 241
11.4 KUHN S ALGORITHM 245
11.5 CONVERGENCE PROOFS 250
11.6 COMPLEXITY ANALYSIS AND NUMERICAL EXAMPLES 260
12 GROEBNER BASES FOR SOLVING POLYNOMIAL EQUATIONS 265
12.1 INTRODUCTION 265
12.2 BASIC CONCEPTS AND HILBERT S BASIS THEOREM 266
12.3 MULTI-VARIABLE DIVISION ALGORITHM 269
12.4 GROEBNER BASES 273
12.5 BUCHBERGER S ALGORITHM 275
12.6 HILBERT S ZERO POINT THEOREM 282
12.7 APPLICATIONS: THE COMPLEMENTARITY PROBLEMS 286
13 INTERSECTION THEORY 289
13.1 INTRODUCTION 289
13.2 A GENERAL INTERSECTION THEOREM 290
13.3 INTERSECTION THEOREMS ON THE UNIT SIMPLEX 293
13.4 INTERSECTION THEOREMS ON POLYTOPES 296
13.5 THEOREMS WITH MULTIPLE INTERSECTION POINTS 301
13.6 AN M.P.B. INTERSECTION THEOREM 302
13.7 HELLY S INTERSECTION THEOREM 308
14 SPERNER THEORY 311
14.1 INTRODUCTION 311
14.2 PRELIMINARIES FOR ANALYSIS 312
14.3 MAIN INTEGER LABELING THEOREMS 313
14.4 APPLICATIONS TO THE UNIT SIMPLEX 317
14.5 APPLICATIONS TO POLYTOPES 320
REFERENCES 323
INDEX 335
|
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| spelling | Yang, Zaifu 1965- Verfasser (DE-588)171191722 aut Computing equilibria and fixed points the solution of nonlinear inequalities by Zaifu Yang Boston [u.a.] Kluwer 1999 X, 341 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier [Theory and decision library / C] 21 Algoritmen gtt Fixed point theoremas gtt Functietheorie gtt Gröbner, Bases de ram Jeux, Théorie des ram Manifolds gtt Mathématiques économiques ram Point fixe, Théorème du ram Speltheorie gtt Fixed point theory Game theory Gröbner bases Fixpunkt (DE-588)4154496-1 gnd rswk-swf Fixpunkt-Methode (DE-588)4139170-6 gnd rswk-swf Fixpunkt-Methode (DE-588)4139170-6 s DE-604 Fixpunkt (DE-588)4154496-1 s C] [Theory and decision library 21 (DE-604)BV000736902 21 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008398165&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yang, Zaifu 1965- Computing equilibria and fixed points the solution of nonlinear inequalities Algoritmen gtt Fixed point theoremas gtt Functietheorie gtt Gröbner, Bases de ram Jeux, Théorie des ram Manifolds gtt Mathématiques économiques ram Point fixe, Théorème du ram Speltheorie gtt Fixed point theory Game theory Gröbner bases Fixpunkt (DE-588)4154496-1 gnd Fixpunkt-Methode (DE-588)4139170-6 gnd |
| subject_GND | (DE-588)4154496-1 (DE-588)4139170-6 |
| title | Computing equilibria and fixed points the solution of nonlinear inequalities |
| title_auth | Computing equilibria and fixed points the solution of nonlinear inequalities |
| title_exact_search | Computing equilibria and fixed points the solution of nonlinear inequalities |
| title_full | Computing equilibria and fixed points the solution of nonlinear inequalities by Zaifu Yang |
| title_fullStr | Computing equilibria and fixed points the solution of nonlinear inequalities by Zaifu Yang |
| title_full_unstemmed | Computing equilibria and fixed points the solution of nonlinear inequalities by Zaifu Yang |
| title_short | Computing equilibria and fixed points |
| title_sort | computing equilibria and fixed points the solution of nonlinear inequalities |
| title_sub | the solution of nonlinear inequalities |
| topic | Algoritmen gtt Fixed point theoremas gtt Functietheorie gtt Gröbner, Bases de ram Jeux, Théorie des ram Manifolds gtt Mathématiques économiques ram Point fixe, Théorème du ram Speltheorie gtt Fixed point theory Game theory Gröbner bases Fixpunkt (DE-588)4154496-1 gnd Fixpunkt-Methode (DE-588)4139170-6 gnd |
| topic_facet | Algoritmen Fixed point theoremas Functietheorie Gröbner, Bases de Jeux, Théorie des Manifolds Mathématiques économiques Point fixe, Théorème du Speltheorie Fixed point theory Game theory Gröbner bases Fixpunkt Fixpunkt-Methode |
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