Pathways to solutions, fixed points and equilibria:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Englewood CLiffs, NJ
Prentice-Hall
1981
|
| Schriftenreihe: | Prentice-Hall series in computational mathematics.
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 479 S. graph. Darst. |
| ISBN: | 0136535011 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV002140967 | ||
| 003 | DE-604 | ||
| 005 | 20210726 | ||
| 007 | t | ||
| 008 | 890928s1981 d||| |||| 00||| eng d | ||
| 020 | |a 0136535011 |9 0-13-653501-1 | ||
| 035 | |a (OCoLC)7461860 | ||
| 035 | |a (DE-599)BVBBV002140967 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G |a DE-703 |a DE-384 |a DE-739 |a DE-188 | ||
| 050 | 0 | |a QA371 | |
| 082 | 0 | |a 515/.252 |2 19 | |
| 082 | 0 | |a 515.3/5 |2 19 | |
| 084 | |a SK 280 |0 (DE-625)143228: |2 rvk | ||
| 084 | |a SK 910 |0 (DE-625)143270: |2 rvk | ||
| 100 | 1 | |a Zangwill, Willard I. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Pathways to solutions, fixed points and equilibria |c Willard I. Zangwill ; C. B. Garcia* |
| 264 | 1 | |a Englewood CLiffs, NJ |b Prentice-Hall |c 1981 | |
| 300 | |a XV, 479 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Prentice-Hall series in computational mathematics. | |
| 650 | 7 | |a Differentiaalvergelijkingen |2 gtt | |
| 650 | 7 | |a Fixed point theoremas |2 gtt | |
| 650 | 7 | |a Numerieke methoden |2 gtt | |
| 650 | 4 | |a Differential equations |x Numerical solutions | |
| 650 | 4 | |a Fixed point theory | |
| 700 | 1 | |a Garcia, C. B. |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001404146&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-001404146 | ||
Datensatz im Suchindex
| _version_ | 1804116595165888512 |
|---|---|
| adam_text | Contents
FOREWORD xi
PREFACE xiii
|| 11| BASIC THEORY 7
|| 11| SOLUTIONS, HOMOTOPIES, AND PATHS 3
1.1 Solving Equations 3 1.2 The Homotopy Principle 4
1.3 Varieties of Homotopies 12 1.4 Path Existence 14 Summary 20
Exercises 21 Notes 23
2 THE BASIC DIFFERENTIAL EQUATIONS 24
2.1 Movement along a Path 24 2.2 Orientation 30 2.3 The Piecewise Case 33
Summary 34 Appendix 35 Exercises 40 Notes 42
iv Contents
||31| FIXED POINTS, EQUATIONS,
AND DEGREE THEORY 43
3.1 Preliminaries 43 3.2 Fixed Point Theorems 46 3.3 Nonlinear Equations 51
3.4 Degree Theory 52 Exercises 57 Notes 60
|| III APPLICATIONS 61
|4| NONLINEAR PROGRAMMING : DYNAMIC,
PARAMETRIC, AND ALGORITHMIC 63
4.1 Statement of NLP 64 4.2 The Kuhn Tucker Equations 65
4.3 Dynamic and Parametric NLP 68 4.4 Path Existence for the Dynamic NLP 71
4.5 Solving the NLP by Path Following 72 Summary 78 Exercises 78 Notes 79
||5|| EQUILIBRIUM PROGRAMMING 81
5.1 The Equilibrium Programming Problem 81
5.2 Nonlinear Programming versus Equilibrium Programming 84
5.3 Examples of EP 86 5.4 Proof of Equilibrium Point Existence 96
5.5 The Dynamic EP 99 5.6 The Algorithm 100 Summary 105 Appendix 106
Exercises 107 Notes 110
||6|| ECONOMIC EQUILIBRIA 112
6.1 The Economic Equilibrium Model 112 6.2 Transforming EE into EP 116
6.3 Competitive Equilibrium Extended 125 6.4 The Pricing Out Mechanism 128
Summary 128 Appendix 128 Exercises 130 Notes 131
||7|| OBTAINING THE COMPETITIVE EQUILIBRIUM 132
7.1 The Edgeworth Box 132 7.2 Obtaining the Competitive Equilibrium 139
7.3 Equilibrium for M Individuals 143 Summary 144 Exercises 145 Notes 145
||8|| GAME THEORY 147
8.1 Two Person Games 147 8.2 Mixed Strategies 151 8.3 Af Person Games 155
8.4 Some Dilemmas Concerning the Equilibrium Concept 160 Summary 164
Exercises 164 Notes 165
Contents v
||9|| NETWORK EQUILIBRIUM AND ELASTICITY 166
9.1 Network Equilibrium Introduced 166
9.2 The Paradox of Adding or Removing a Link 174
9.3 Formulation of the Network Equilibrium Model 178
9.4 The Equilibrium Programming Formulation 181
9.5 Existence of a Network Equilibrium 184 9.6 An Important Special Case 186
9.7 Elasticity and Strength of Materials 189 Summary 195 Exercises 195
Notes 196
||10|| CATASTROPHE THEORY 198
10.1 Unconstrained Catastrophes 198 10.2 Second Order Conditions 203
10.3 Other Forms of Catastrophe 209 Exercises 214 Notes 215
|| III || ALGORITHMS AND
SOLUTION PROCEDURES 277
H11 || PATH FOLLOWING ALGORITHMS 219
Overview of Part III 219 Simplicial Algorithms 220
11.1 Getting Started 220 11.2 Simplices 222 11.3 Functions on Simplices 224
11.4 Creating a Path 227 11.5 Simplicial Algorithms 230 Summary 000
Appendix 234 Exercises 238 Notes 239
1|12|| THE FLEX SIMPLICIAL ALGORITHM 240
12.1 Notation 240 12.2 Behavior of the Flex Simplicial 241
12.3 Prevention of Cycling 244 12.4 Large Simplices 246 Summary 252
Appendix 252 Exercises 254 Notes 255
i || 13 j| TRIANGULATION ALGORITHMS 257
13.1 The Triangulation 257 13.2 The Triangulation Algorithm 259
13.3 Complementarity 262 Exercises 265 Notes 267
vi Contents
||14|| INTEGER LABELS 268
14.1 A Trivial Piecewise Linear Map 269 14.2 The Integer Algorithm 272
14.3 Sperner s Lemma 275
14.4 The Knaster Kuratowski Mazurkiewicz Lemma 283 Summary 286
Exercises 286 Notes 288
!| 151| DIFFERENTIAL EQUATIONS 289
15.1 Euler s Method 289 15.2 The Homotopy Differential Equations 291
15.3 Trouble with Euler and Possible Alternatives 295 15.4 A Restart Method 297
15.5 Newton s Solution Method 300 Summary 306 Appendix 306
Exercises 308 Notes 309
|| 161| PREDICTOR CORRECTOR METHODS 310
16.1 The Basic Idea of Predictor Corrector Methods 310
16.2 Horizontal Corrector 315 16.3 Failure of the Horizontal Corrector 317
16A The Euler Predictor Corrector Algorithm 320 16.5 General Discussion 322
Summary 323 Exercises 324 Notes 325
|| 171| SPECIAL FUNCTIONS: CONTRACTION
AND SEPARABILITY 326
17.1 Contraction 326 17.2 Separable Homotopies 329 17.3 Example 335
Summary 338 Exercises 339 Notes 340
IV FUNDAMENTAL CONCEPTS
AND EXTENSIONS 341
|| 181| ALL SOLUTIONS 343
18.1 Complex Spaces 344 18.2 Development of the Homotopy 350
18.3 Conditions for Path Finiteness 354 18.4 Further Considerations 359
Summary 361 Exercises 362 Notes 363
||19|| THE LINEAR COMPLEMENTARITY PROBLEM 364
19.1 The Linear Complementarity Problem 364
19.2 Solving the LC by Path Following 368 19.3 Lemke s Method 371
Summary 379 Exercises 379 Notes 380
Contents vii
||201| LINEAR COMPLEMENTARITY IN ACTION 381
20.1 Existence of an LC Solution 381 20.2 Quadratic Programs 384
20.3 Bimatrix Games 388 Summary 394 Exercises 394 Notes 396
I! 21 || THE KAKUTANI THEOREM
AND THE ECONOMIC EQUILIBRIUM REVISITED 397
21.1 Point to Set Maps 397 21.2 The Kakutani Theorem 403
21.3 Economic Equilibrium Existence Revisited 409 Summary 416
Exercises 416 Notes 418
|| 221| RELAXATION OF REGULARITY
AND DIFFERENTIABILITY 475
22.1 The Two Main Theorems 420 22.2 The Weierstrass Theorem 425
22.3 Applying the Sard and Weierstrass Theorems 427
22.4 Assumption Relaxation for the Homotopy Invariance Theorem and the Fixed
Point Theorem 428 22.5 Fixed Point Theorems 434 22.6 Overview 435
Summary 435 Appendices 436 Exercises 441 Notes 442
||A|| APPENDIX A: DERIVATIVES AND
DIFFERENTIAL EQUATIONS 443
A.I Functions 443 A.2 Mean Value Theorems 445
A.3 The Implicit Function Theorem 446
A.4 Existence and Uniqueness of Solutions for Ordinary Differential Equations 448
|| B || APPENDIX B: CONVEXITY 450
B.I Convex Sets 450 B.2 Convex and Concave Functions 451
|| C || APPENDIX C: THE KUHN TUCKER
CONDITIONS 455
C.I The Nonlinear Programming Problem 455
C.2 The Kuhn Tucker Necessary Conditions 456
C.3 Sufficiency of the K T Conditions 457
BIBLIOGRAPHY 459
AUTHOR INDEX 473
INDEX 476
|
| any_adam_object | 1 |
| author | Zangwill, Willard I. Garcia, C. B. |
| author_facet | Zangwill, Willard I. Garcia, C. B. |
| author_role | aut aut |
| author_sort | Zangwill, Willard I. |
| author_variant | w i z wi wiz c b g cb cbg |
| building | Verbundindex |
| bvnumber | BV002140967 |
| callnumber-first | Q - Science |
| callnumber-label | QA371 |
| callnumber-raw | QA371 |
| callnumber-search | QA371 |
| callnumber-sort | QA 3371 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 280 SK 910 |
| ctrlnum | (OCoLC)7461860 (DE-599)BVBBV002140967 |
| dewey-full | 515/.252 515.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.252 515.3/5 |
| dewey-search | 515/.252 515.3/5 |
| dewey-sort | 3515 3252 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01543nam a2200409 c 4500</leader><controlfield tag="001">BV002140967</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20210726 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">890928s1981 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0136535011</subfield><subfield code="9">0-13-653501-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)7461860</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV002140967</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA371</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.252</subfield><subfield code="2">19</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.3/5</subfield><subfield code="2">19</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 280</subfield><subfield code="0">(DE-625)143228:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 910</subfield><subfield code="0">(DE-625)143270:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Zangwill, Willard I.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Pathways to solutions, fixed points and equilibria</subfield><subfield code="c">Willard I. Zangwill ; C. B. Garcia*</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Englewood CLiffs, NJ</subfield><subfield code="b">Prentice-Hall</subfield><subfield code="c">1981</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XV, 479 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Prentice-Hall series in computational mathematics.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Differentiaalvergelijkingen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Fixed point theoremas</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Numerieke methoden</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential equations</subfield><subfield code="x">Numerical solutions</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fixed point theory</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Garcia, C. B.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001404146&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-001404146</subfield></datafield></record></collection> |
| id | DE-604.BV002140967 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:41:00Z |
| institution | BVB |
| isbn | 0136535011 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001404146 |
| oclc_num | 7461860 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-703 DE-384 DE-739 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-703 DE-384 DE-739 DE-188 |
| physical | XV, 479 S. graph. Darst. |
| publishDate | 1981 |
| publishDateSearch | 1981 |
| publishDateSort | 1981 |
| publisher | Prentice-Hall |
| record_format | marc |
| series2 | Prentice-Hall series in computational mathematics. |
| spelling | Zangwill, Willard I. Verfasser aut Pathways to solutions, fixed points and equilibria Willard I. Zangwill ; C. B. Garcia* Englewood CLiffs, NJ Prentice-Hall 1981 XV, 479 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Prentice-Hall series in computational mathematics. Differentiaalvergelijkingen gtt Fixed point theoremas gtt Numerieke methoden gtt Differential equations Numerical solutions Fixed point theory Garcia, C. B. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001404146&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zangwill, Willard I. Garcia, C. B. Pathways to solutions, fixed points and equilibria Differentiaalvergelijkingen gtt Fixed point theoremas gtt Numerieke methoden gtt Differential equations Numerical solutions Fixed point theory |
| title | Pathways to solutions, fixed points and equilibria |
| title_auth | Pathways to solutions, fixed points and equilibria |
| title_exact_search | Pathways to solutions, fixed points and equilibria |
| title_full | Pathways to solutions, fixed points and equilibria Willard I. Zangwill ; C. B. Garcia* |
| title_fullStr | Pathways to solutions, fixed points and equilibria Willard I. Zangwill ; C. B. Garcia* |
| title_full_unstemmed | Pathways to solutions, fixed points and equilibria Willard I. Zangwill ; C. B. Garcia* |
| title_short | Pathways to solutions, fixed points and equilibria |
| title_sort | pathways to solutions fixed points and equilibria |
| topic | Differentiaalvergelijkingen gtt Fixed point theoremas gtt Numerieke methoden gtt Differential equations Numerical solutions Fixed point theory |
| topic_facet | Differentiaalvergelijkingen Fixed point theoremas Numerieke methoden Differential equations Numerical solutions Fixed point theory |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001404146&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT zangwillwillardi pathwaystosolutionsfixedpointsandequilibria AT garciacb pathwaystosolutionsfixedpointsandequilibria |