Generalized semi-infinite optimization and related topics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Lemgo
Heldermann
2003
|
| Series: | Research and exposition in mathematics
29 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXI, 361 S. graph. Darst |
| ISBN: | 3885382296 |
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Record in the Search Index
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| adam_text | RESEARCH AND EXPOSITION IN MATHEMATICS VOLUME 29 GERHARD-WILHELM WEBER
GENERALIZED SEMI-INFINITE OPTIMIZATION AND RELATED TOPICS HELDERMANN
VERLAG CONTENTS CONTENTS IX INTRODUCTION XIII 1 REPRESENTATIONS AND
OPTIMALITY 1 1.1 FORMULATION AND MOTIVATION 1 1.2 PROBLEM REPRESENTATION
(APPROACH I) 10 1.3 OPTIMALITY CONDITIONS (APPROACH I) 22 1.4 PROBLEM
REPRESENTATIONS (APPROACH II) 30 1.5 OPTIMALITY CONDITIONS (APPROACH II)
38 1.6 CONCLUDING REMARKS 44 2 TOPOLOGICAL AND STABILITY PROPERTIES 47
2.1 SOME MOTIVATIONS FROM TOPOLOGY 47 2.2 STABILITY OF THE FEASIBLE SET
(APPROACH I) 54 2.3 STRUCTURAL STABILITY OF THE PROBLEM (APPROACH I) .
67 2.3.1 CHARACTERIZATION THEOREM ON STRUCTURAL STABILITY 68 2.3.2
STRONG STABILITY AND PROOF OF THE CHARACTERIZATION THEOREM . . 77
2.3.2.1 STRONG STABILITY 77 2.3 J .2.2 PROOF OF THE CHARACTERIZATION
THEOREM 83 2.4 GENERALIZED RESULTS (APPROACH I) 97 2.4.1 EXCISIONAL
(TOPOLOGICAL) STABILITY AND ITS CHARACTERIZATION FOR UNBOUNDED FEASIBLE
SETS 97 2.4.2 STRUCTURAL STABILITY AND ITS CHARACTERIZATION IN CASE OF
MAX- TYPE OBJECTIVE FUNCTIONS 103 CONTENTS 2.4.3 EXCISIONAL STRUCTURAL
STABILITY AND ITS CHARACTERIZATION IN CASE OF MAX-TYPE OBJECTIVE
FUNCTIONS 112 2.5 FURTHER TOPOLOGICAL ASPECTS (APPROACHES I, II) 116 2.6
CONCLUDING REMARKS 118 3 CONCEPTS OF ITERATION PROCEDURES 121 3.1 A
PROCEDURE BASED ON DISCRETIZATION (APPR. I) 122 3.2 PROCEDURES BASED ON
SUBPROBLEMS (APPR. II) . . . 134 3.2.1 FIRST THEORETICAL TREATMENT 135
3.2.2 MORE PRACTICAL TREATMENT BASED ON LINEARIZATION 144 3.2.3 SECOND
THEORETICAL TREATMENT (APPR. I IN APPR. II) 147 3.2.4 TWO-LEVEL
TREATMENT 149 3.3 A PROCEDURE BASED ON LOCAL LINEARIZATIONS (APPR. ILL)
151 3.3.1 INTRODUCTION ^ 151 3.3.2 ITERATION PROCEDURE AND ITS
TOPOLOGICAL BACKGROUND 155 3.3.3 CONVERGENCE THEOREM 170 3.3.4 CRITICISM
174 3.4 CONCLUDING REMARKS 174 4 OPTIMAL CONTROL AND DISCRETE
MATHEMATICS 177 4.1 OPTIMAL CONTROL OF ORDINARY DIFFERENTIAL EQUATIONS
178 4.1.1 INTRODUCTION INTO THE STRUCTURAL INVESTIGATION 178 4.1.2 THE
PARTICULAR STRUCTURE AND ITS STABILITY . 185 4.1.3 COMPOSITE STRUCTURE;
FOUNDATIONS 195 4.1.4 THE COMPOSITE STRUCTURE; AN UNFOLDING 209 4.1.4.1
MODELLING THEOREM 209 4.1.4.2 STRUCTURAL TRANSVERSALITY AND CORE
FUNCTIONS 209 4.1.4.3 GENERALIZED SEMI-INFINITE OPTIMIZATION 226 4.1.4.4
STRUCTURAL EQUIVALENCES AND COMPLETENESS 235 4.1.5 COMPOSITE STRUCTURAL
STABILITY; A CONCLUSION 244 4.1.5.1 COMPOSITE STRUCTURAL STABILITY 244
CONTENTS 4.1.5.2 THEOREM OF COMPLETENESS AND CHARACTERIZATION .... 245
4.1.5.3 CONCLUDING REMARKS 250 4.1.6 DECOMPOSITE STRUCTURE AND ITS
STABILITY 251 4.1.6.1 DECOMPOSITE STRUCTURE 251 4.1.6.2 DECOMPOSITE
STRUCTURAL STABILITY 252 4.1.6.3 THEOREM ON COMPLETENESS AND
CHARACTERIZATION .... 254 4.1.7 CONCLUDING REMARK 255 4.2 TIME-MINIMAL
CONTROL AND DISCRETE MATHEMATICS 257 4.2.1 A PROBLEM OF TIME-MINIMAL
CONTROL AND ITS TREATMENT 257 4.2.1.1 PROBLEM FORMULATION 257 4.2.1.2
PROBLEM DECOMPOSITION 258 4.2.1.3 PROBLEM TREATMENT 261 4.2.1.4
CONCLUDING EVALUATIONS 267 4.2.2 CONNECTIONS WITH DISCRETE MATHEMATICS
270 4.2.2.1 RELATIONS TO UNDIRECTED GRAPHS 270 4.2.2.2 RELATIONS TO
DIRECTED GRAPHS 278 4.2.2.3 RELATIONS TO RANDOM GRAPHS 289 4.2.2.4
RELATIONS TO NEWTON METHODS 293 4.2.3 CONCLUDING REMARKS 298 APPENDIX
299 LIST OF FIGURES AND TABLES 309 BIBLIOGRAPHY 311 GLOSSARY OF SYMBOLS
AND ABBREVIATIONS 333 INDEX 350
|
| adam_txt |
RESEARCH AND EXPOSITION IN MATHEMATICS VOLUME 29 GERHARD-WILHELM WEBER
GENERALIZED SEMI-INFINITE OPTIMIZATION AND RELATED TOPICS HELDERMANN
VERLAG CONTENTS CONTENTS IX INTRODUCTION XIII 1 REPRESENTATIONS AND
OPTIMALITY 1 1.1 FORMULATION AND MOTIVATION 1 1.2 PROBLEM REPRESENTATION
(APPROACH I) 10 1.3 OPTIMALITY CONDITIONS (APPROACH I) 22 1.4 PROBLEM
REPRESENTATIONS (APPROACH II) 30 1.5 OPTIMALITY CONDITIONS (APPROACH II)
38 1.6 CONCLUDING REMARKS 44 2 TOPOLOGICAL AND STABILITY PROPERTIES 47
2.1 SOME MOTIVATIONS FROM TOPOLOGY 47 2.2 STABILITY OF THE FEASIBLE SET
(APPROACH I) 54 2.3 STRUCTURAL STABILITY OF THE PROBLEM (APPROACH I) .
67 2.3.1 CHARACTERIZATION THEOREM ON STRUCTURAL STABILITY 68 2.3.2
STRONG STABILITY AND PROOF OF THE CHARACTERIZATION THEOREM . . 77
2.3.2.1 STRONG STABILITY 77 2.3 J .2.2 PROOF OF THE CHARACTERIZATION
THEOREM 83 2.4 GENERALIZED RESULTS (APPROACH I) 97 2.4.1 EXCISIONAL
(TOPOLOGICAL) STABILITY AND ITS CHARACTERIZATION FOR UNBOUNDED FEASIBLE
SETS 97 2.4.2 STRUCTURAL STABILITY AND ITS CHARACTERIZATION IN CASE OF
MAX- TYPE OBJECTIVE FUNCTIONS 103 CONTENTS 2.4.3 EXCISIONAL STRUCTURAL
STABILITY AND ITS CHARACTERIZATION IN CASE OF MAX-TYPE OBJECTIVE
FUNCTIONS 112 2.5 FURTHER TOPOLOGICAL ASPECTS (APPROACHES I, II) 116 2.6
CONCLUDING REMARKS 118 3 CONCEPTS OF ITERATION PROCEDURES 121 3.1 A
PROCEDURE BASED ON DISCRETIZATION (APPR. I) 122 3.2 PROCEDURES BASED ON
SUBPROBLEMS (APPR. II) . . . 134 3.2.1 FIRST THEORETICAL TREATMENT 135
3.2.2 MORE PRACTICAL TREATMENT BASED ON LINEARIZATION 144 3.2.3 SECOND
THEORETICAL TREATMENT (APPR. I IN APPR. II) 147 3.2.4 TWO-LEVEL
TREATMENT 149 3.3 A PROCEDURE BASED ON LOCAL LINEARIZATIONS (APPR. ILL)
151 3.3.1 INTRODUCTION ^ 151 3.3.2 ITERATION PROCEDURE AND ITS
TOPOLOGICAL BACKGROUND 155 3.3.3 CONVERGENCE THEOREM 170 3.3.4 CRITICISM
174 3.4 CONCLUDING REMARKS 174 4 OPTIMAL CONTROL AND DISCRETE
MATHEMATICS 177 4.1 OPTIMAL CONTROL OF ORDINARY DIFFERENTIAL EQUATIONS
178 4.1.1 INTRODUCTION INTO THE STRUCTURAL INVESTIGATION 178 4.1.2 THE
PARTICULAR STRUCTURE AND ITS STABILITY . 185 4.1.3 COMPOSITE STRUCTURE;
FOUNDATIONS 195 4.1.4 THE COMPOSITE STRUCTURE; AN UNFOLDING 209 4.1.4.1
MODELLING THEOREM 209 4.1.4.2 STRUCTURAL TRANSVERSALITY AND CORE
FUNCTIONS 209 4.1.4.3 GENERALIZED SEMI-INFINITE OPTIMIZATION 226 4.1.4.4
STRUCTURAL EQUIVALENCES AND COMPLETENESS 235 4.1.5 COMPOSITE STRUCTURAL
STABILITY; A CONCLUSION 244 4.1.5.1 COMPOSITE STRUCTURAL STABILITY 244
CONTENTS 4.1.5.2 THEOREM OF COMPLETENESS AND CHARACTERIZATION . 245
4.1.5.3 CONCLUDING REMARKS 250 4.1.6 DECOMPOSITE STRUCTURE AND ITS
STABILITY 251 4.1.6.1 DECOMPOSITE STRUCTURE 251 4.1.6.2 DECOMPOSITE
STRUCTURAL STABILITY 252 4.1.6.3 THEOREM ON COMPLETENESS AND
CHARACTERIZATION . 254 4.1.7 CONCLUDING REMARK 255 4.2 TIME-MINIMAL
CONTROL AND DISCRETE MATHEMATICS 257 4.2.1 A PROBLEM OF TIME-MINIMAL
CONTROL AND ITS TREATMENT 257 4.2.1.1 PROBLEM FORMULATION 257 4.2.1.2
PROBLEM DECOMPOSITION 258 4.2.1.3 PROBLEM TREATMENT 261 4.2.1.4
CONCLUDING EVALUATIONS 267 4.2.2 CONNECTIONS WITH DISCRETE MATHEMATICS
270 4.2.2.1 RELATIONS TO UNDIRECTED GRAPHS 270 4.2.2.2 RELATIONS TO
DIRECTED GRAPHS 278 4.2.2.3 RELATIONS TO RANDOM GRAPHS 289 4.2.2.4
RELATIONS TO NEWTON METHODS 293 4.2.3 CONCLUDING REMARKS 298 APPENDIX
299 LIST OF FIGURES AND TABLES 309 BIBLIOGRAPHY 311 GLOSSARY OF SYMBOLS
AND ABBREVIATIONS 333 INDEX 350 |
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| index_date | 2024-07-02T16:16:39Z |
| indexdate | 2024-07-09T20:51:03Z |
| institution | BVB |
| isbn | 3885382296 |
| language | English |
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| physical | XXI, 361 S. graph. Darst |
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| series | Research and exposition in mathematics |
| series2 | Research and exposition in mathematics |
| spelling | Weber, Gerhard-Wilhelm 1960- Verfasser (DE-588)113368178 aut Generalized semi-infinite optimization and related topics Gerhard-Wilhelm Weber Lemgo Heldermann 2003 XXI, 361 S. graph. Darst txt rdacontent n rdamedia nc rdacarrier Research and exposition in mathematics 29 Zugl.: Darmstadt, Techn. Univ., Habil.-Schr., 1999 Mathematical optimization Semiinfinite Optimierung (DE-588)4137036-3 gnd rswk-swf Diskrete Mathematik (DE-588)4129143-8 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Optimale Kontrolle (DE-588)4121428-6 s DE-604 Diskrete Mathematik (DE-588)4129143-8 s Semiinfinite Optimierung (DE-588)4137036-3 s Research and exposition in mathematics 29 (DE-604)BV000017533 29 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015344019&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Weber, Gerhard-Wilhelm 1960- Generalized semi-infinite optimization and related topics Research and exposition in mathematics Mathematical optimization Semiinfinite Optimierung (DE-588)4137036-3 gnd Diskrete Mathematik (DE-588)4129143-8 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| subject_GND | (DE-588)4137036-3 (DE-588)4129143-8 (DE-588)4121428-6 (DE-588)4113937-9 |
| title | Generalized semi-infinite optimization and related topics |
| title_auth | Generalized semi-infinite optimization and related topics |
| title_exact_search | Generalized semi-infinite optimization and related topics |
| title_exact_search_txtP | Generalized semi-infinite optimization and related topics |
| title_full | Generalized semi-infinite optimization and related topics Gerhard-Wilhelm Weber |
| title_fullStr | Generalized semi-infinite optimization and related topics Gerhard-Wilhelm Weber |
| title_full_unstemmed | Generalized semi-infinite optimization and related topics Gerhard-Wilhelm Weber |
| title_short | Generalized semi-infinite optimization and related topics |
| title_sort | generalized semi infinite optimization and related topics |
| topic | Mathematical optimization Semiinfinite Optimierung (DE-588)4137036-3 gnd Diskrete Mathematik (DE-588)4129143-8 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| topic_facet | Mathematical optimization Semiinfinite Optimierung Diskrete Mathematik Optimale Kontrolle Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015344019&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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