Stochastic global optimization:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2008
|
| Schriftenreihe: | Springer optimization and its applications
9 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Fälschlich als Bd. 1 der Serie bezeichnet |
| Beschreibung: | IX, 262 S. graph. Darst. |
| ISBN: | 9780387740225 0387740228 9780387747408 |
Internformat
MARC
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| 245 | 1 | 0 | |a Stochastic global optimization |c Anatoly Zhigljavsky ; Antanasz Žilinskas |
| 264 | 1 | |a New York, NY |b Springer |c 2008 | |
| 300 | |a IX, 262 S. |b graph. Darst. | ||
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| 490 | 1 | |a Springer optimization and its applications |v 9 | |
| 500 | |a Fälschlich als Bd. 1 der Serie bezeichnet | ||
| 650 | 4 | |a Optimisation mathématique | |
| 650 | 4 | |a Processus stochastiques | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 0 | 7 | |a Globale Optimierung |0 (DE-588)4140067-7 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804137770359193600 |
|---|---|
| adam_text | Contents
Introduction 1
Notation 3
1 Basic Concepts and Ideas 5
1.1 The Scope of Global Optimization 5
1.1.1 General Minimization Problem 5
1.1.2 Global Minimization Versus Local Minimization 8
1.1.3 Combining Locality and Globality of Search 10
1.1.4 Theory and Heuristics 12
1.2 Stochastic Methods 13
1.2.1 Determinism Versus Stochasticity 14
1.2.2 Methods Based on Statistical Models 17
1.2.3 Basic Ideas of Global Random Search 18
1.3 Testing, Software and Applications 19
1.3.1 Testing 19
1.3.2 Software 22
1.3.3 Applications 23
2 Global Random Search: Fundamentals and Statistical
Inference 29
2.1 Introduction to Global Random Search 29
2.1.1 Main Assumptions 29
2.1.2 Formal Scheme of Global Random Search Algorithms . . 33
2.1.3 Convergence of Global Random Search Algorithms .... 34
2.1.4 Random Errors in Observations 36
2.2 Pure Random and Pure Adaptive Search Algorithms 38
2.2.1 Pure Random Search and the Associated c.d.f 38
2.2.2 Rate of Convergence of Pure Random Search 41
2.2.3 Pure Adaptive Search and Related Methods 48
2.2.4 Pure Adaptive Search of Order k 50
flll Contents
2.3 Order Statistics and Record Values: Probabilistic Aspects .... 51
2.3.1 Order Statistics: Non-Asymptotic Properties 52
2.3.2 Extreme Order Statistics: Asymptotic Properties 54
2.3.3 Record Values and Record Moments 59
2.4 Statistical Inference About m: Known Value of the Tail Index . 64
2.4.1 Estimation of m 65
2.4.2 Confidence Intervals and Hypothesis Testing 73
2.4.3 Choice of n and k 73
2.5 Unknown Value of the Tail Index 75
2.5.1 Statistical Inference 75
2.5.2 Using an Incorrect Value of the Tail Index 77
2.5.3 Exact Determination of the Value of the Tail Index .... 80
2.6 Some Algorithmic and Methodological Aspects 81
2.6.1 Using Statistical Inference in Global Random Search ... 81
2.6.2 Statistical Inference in Random Multistart 85
2.6.3 Sampling on Surfaces 88
2.7 Proofs 90
3 Global Random Search: Extensions 93
3.1 Random and Semi-Random Coverings 93
3.1.1 Covering with Balls and Optimization 94
3.1.2 Dispersion 99
3.1.3 Uniform Sequences and Discrepancies 106
3.2 Comparison of Stratified and Independent Sampling Schemes . 110
3.2.1 Stratified Sampling 110
3.2.2 Asymptotic Criteria 112
3.2.3 Stochastic Dominance with Respect to Record Values . . 114
3.3 Markovian Algorithms 115
3.3.1 Construction of Markovian Algorithms 115
3.3.2 Simulated Annealing 117
3.4 Markov Monotonous Search 122
3.4.1 Statement of the Problem 123
3.4.2 Lower Bounds 128
3.4.3 Homogeneous Search 128
3.5 Methods of Generations 132
3.5.1 Construction of Algorithms and Their Convergence .... 132
3.5.2 Special Cases; Genetic Algorithms 137
3.5.3 Homogeneous Transition Probabilities 141
3.6 Proofs 144
4 Statistical Models 149
4.1 Statistical Models 149
4.1.1 Introduction 149
4.1.2 Random Processes 150
4.1.3 Random Fields 154
Contents IX
4.1.4 Axiomatic Definition of a Statistical Model 155
4.1.5 Response Surfaces 159
4.1.6 Estimation of Parameters 160
4.1.7 Illustrative Comparison 161
4.2 Methods 164
4.2.1 Introduction 164
4.2.2 Passive Methods 166
4.2.3 Bayesian Methods 168
4.2.4 P-algorithm 170
4.2.5 Information Theory Based Approach 174
4.2.6 Response Surface Based Methods 176
4.2.7 Modifications 180
4.2.8 Proofs of Theorems 181
4.3 One-dimensional Algorithms 184
4.3.1 Introduction 184
4.3.2 One-step Bayesian Algorithm 184
4.3.3 P-algorithm 185
4.3.4 P-algorithm for a Model with Derivatives 188
4.3.5 Comparison of P-algorithms 190
4.3.6 P* -algorithm 192
4.3.7 Convergence 193
4.3.8 Convergence Rates 194
4.3.9 Probabilistic Convergence Rates 200
4.3.10 Testing and Applications 203
4.3.11 Proofs of Theorems and Lemmas 206
4.4 Multidimensional Algorithms 221
4.4.1 Introduction 221
4.4.2 P-algorithm 221
4.4.3 Two Dimensional Select and Clone 224
4.4.4 P-algorithm With Simplicial Partitioning 227
4.4.5 Testing 233
4.4.6 Proofs of Theorems 240
References 245
Index 259
|
| adam_txt |
Contents
Introduction 1
Notation 3
1 Basic Concepts and Ideas 5
1.1 The Scope of Global Optimization 5
1.1.1 General Minimization Problem 5
1.1.2 Global Minimization Versus Local Minimization 8
1.1.3 Combining Locality and Globality of Search 10
1.1.4 Theory and Heuristics 12
1.2 Stochastic Methods 13
1.2.1 Determinism Versus Stochasticity 14
1.2.2 Methods Based on Statistical Models 17
1.2.3 Basic Ideas of Global Random Search 18
1.3 Testing, Software and Applications 19
1.3.1 Testing 19
1.3.2 Software 22
1.3.3 Applications 23
2 Global Random Search: Fundamentals and Statistical
Inference 29
2.1 Introduction to Global Random Search 29
2.1.1 Main Assumptions 29
2.1.2 Formal Scheme of Global Random Search Algorithms . . 33
2.1.3 Convergence of Global Random Search Algorithms . 34
2.1.4 Random Errors in Observations 36
2.2 Pure Random and Pure Adaptive Search Algorithms 38
2.2.1 Pure Random Search and the Associated c.d.f 38
2.2.2 Rate of Convergence of Pure Random Search 41
2.2.3 Pure Adaptive Search and Related Methods 48
2.2.4 Pure Adaptive Search of Order k 50
flll Contents
2.3 Order Statistics and Record Values: Probabilistic Aspects . 51
2.3.1 Order Statistics: Non-Asymptotic Properties 52
2.3.2 Extreme Order Statistics: Asymptotic Properties 54
2.3.3 Record Values and Record Moments 59
2.4 Statistical Inference About m: Known Value of the Tail Index . 64
2.4.1 Estimation of m 65
2.4.2 Confidence Intervals and Hypothesis Testing 73
2.4.3 Choice of n and k 73
2.5 Unknown Value of the Tail Index 75
2.5.1 Statistical Inference 75
2.5.2 Using an Incorrect Value of the Tail Index 77
2.5.3 Exact Determination of the Value of the Tail Index . 80
2.6 Some Algorithmic and Methodological Aspects 81
2.6.1 Using Statistical Inference in Global Random Search . 81
2.6.2 Statistical Inference in Random Multistart 85
2.6.3 Sampling on Surfaces 88
2.7 Proofs 90
3 Global Random Search: Extensions 93
3.1 Random and Semi-Random Coverings 93
3.1.1 Covering with Balls and Optimization 94
3.1.2 Dispersion 99
3.1.3 Uniform Sequences and Discrepancies 106
3.2 Comparison of Stratified and Independent Sampling Schemes . 110
3.2.1 Stratified Sampling 110
3.2.2 Asymptotic Criteria 112
3.2.3 Stochastic Dominance with Respect to Record Values . . 114
3.3 Markovian Algorithms 115
3.3.1 Construction of Markovian Algorithms 115
3.3.2 Simulated Annealing 117
3.4 Markov Monotonous Search 122
3.4.1 Statement of the Problem 123
3.4.2 Lower Bounds 128
3.4.3 Homogeneous Search 128
3.5 Methods of Generations 132
3.5.1 Construction of Algorithms and Their Convergence . 132
3.5.2 Special Cases; Genetic Algorithms 137
3.5.3 Homogeneous Transition Probabilities 141
3.6 Proofs 144
4 Statistical Models 149
4.1 Statistical Models 149
4.1.1 Introduction 149
4.1.2 Random Processes 150
4.1.3 Random Fields 154
Contents IX
4.1.4 Axiomatic Definition of a Statistical Model 155
4.1.5 Response Surfaces 159
4.1.6 Estimation of Parameters 160
4.1.7 Illustrative Comparison 161
4.2 Methods 164
4.2.1 Introduction 164
4.2.2 Passive Methods 166
4.2.3 Bayesian Methods 168
4.2.4 P-algorithm 170
4.2.5 Information Theory Based Approach 174
4.2.6 Response Surface Based Methods 176
4.2.7 Modifications 180
4.2.8 Proofs of Theorems 181
4.3 One-dimensional Algorithms 184
4.3.1 Introduction 184
4.3.2 One-step Bayesian Algorithm 184
4.3.3 P-algorithm 185
4.3.4 P-algorithm for a Model with Derivatives 188
4.3.5 Comparison of P-algorithms 190
4.3.6 P* -algorithm 192
4.3.7 Convergence 193
4.3.8 Convergence Rates 194
4.3.9 Probabilistic Convergence Rates 200
4.3.10 Testing and Applications 203
4.3.11 Proofs of Theorems and Lemmas 206
4.4 Multidimensional Algorithms 221
4.4.1 Introduction 221
4.4.2 P-algorithm 221
4.4.3 Two Dimensional Select and Clone 224
4.4.4 P-algorithm With Simplicial Partitioning 227
4.4.5 Testing 233
4.4.6 Proofs of Theorems 240
References 245
Index 259 |
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| id | DE-604.BV023392352 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:20:29Z |
| indexdate | 2024-07-09T21:17:34Z |
| institution | BVB |
| isbn | 9780387740225 0387740228 9780387747408 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016575272 |
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| owner_facet | DE-824 DE-11 |
| physical | IX, 262 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series | Springer optimization and its applications |
| series2 | Springer optimization and its applications |
| spelling | Žigljavskij, Anatolij Aleksandrovič 1953- Verfasser (DE-588)124189199 aut Stochastic global optimization Anatoly Zhigljavsky ; Antanasz Žilinskas New York, NY Springer 2008 IX, 262 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer optimization and its applications 9 Fälschlich als Bd. 1 der Serie bezeichnet Optimisation mathématique Processus stochastiques Mathematical optimization Stochastic processes Globale Optimierung (DE-588)4140067-7 gnd rswk-swf Stochastische Optimierung (DE-588)4057625-5 gnd rswk-swf Stochastische Optimierung (DE-588)4057625-5 s Globale Optimierung (DE-588)4140067-7 s DE-604 Žilinskas, Antanas 1946- Verfasser (DE-588)133388670 aut Springer optimization and its applications 9 (DE-604)BV021746093 9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016575272&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Žigljavskij, Anatolij Aleksandrovič 1953- Žilinskas, Antanas 1946- Stochastic global optimization Springer optimization and its applications Optimisation mathématique Processus stochastiques Mathematical optimization Stochastic processes Globale Optimierung (DE-588)4140067-7 gnd Stochastische Optimierung (DE-588)4057625-5 gnd |
| subject_GND | (DE-588)4140067-7 (DE-588)4057625-5 |
| title | Stochastic global optimization |
| title_auth | Stochastic global optimization |
| title_exact_search | Stochastic global optimization |
| title_exact_search_txtP | Stochastic global optimization |
| title_full | Stochastic global optimization Anatoly Zhigljavsky ; Antanasz Žilinskas |
| title_fullStr | Stochastic global optimization Anatoly Zhigljavsky ; Antanasz Žilinskas |
| title_full_unstemmed | Stochastic global optimization Anatoly Zhigljavsky ; Antanasz Žilinskas |
| title_short | Stochastic global optimization |
| title_sort | stochastic global optimization |
| topic | Optimisation mathématique Processus stochastiques Mathematical optimization Stochastic processes Globale Optimierung (DE-588)4140067-7 gnd Stochastische Optimierung (DE-588)4057625-5 gnd |
| topic_facet | Optimisation mathématique Processus stochastiques Mathematical optimization Stochastic processes Globale Optimierung Stochastische Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016575272&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV021746093 |
| work_keys_str_mv | AT zigljavskijanatolijaleksandrovic stochasticglobaloptimization AT zilinskasantanas stochasticglobaloptimization |