Stochastic decomposition: a statistical method for large scale stochastic linear programming
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1996
|
| Series: | Nonconvex optimization and its applications
8 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXIII, 220 S.: graph. Darst. |
| ISBN: | 0792338405 |
Staff View
MARC
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| 245 | 1 | 0 | |a Stochastic decomposition |b a statistical method for large scale stochastic linear programming |c by Julia L. Higle and Suvrajeet Sen |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1996 | |
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Record in the Search Index
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| adam_text | Contents
Preface xi
Acknowledgements xvii
List of Algorithmic Statements xix
List of Figures xxi
List of Tables xxiii
1. Two Stage Stochastic Linear Programs 1
1.1. Examples of Two Stage Stochastic Linear Programs 3
1.1.1. Capacity Expansion Planning: CEP1 3
1.1.2. Power Generation Planning: PGP2 6
1.1.3. Air Freight Scheduling: STORM 10
1.1.4. Telecommunications Network Planning: SSN 14
1.2. Properties of Two Stage Stochastic Linear Programs 18
1.3. Characteristics of Example Problems 24
1.4. Bibliographical Notes 27
Appendix: CEP1 and PGP2 Data 30
References 32
2. Sampling Within Stochastic Linear Programming ... 35
2.1. Kelley s Cutting Plane Algorithm 37
2.2. Successive Sample Mean Optimization 39
2.3. Issues Related to Sample Based Optimization 46
2.4. Bibliographical Notes 55
Appendix: Data Used in the Illustrative Example 57
viii
References 60
3. Foundations of Stochastic Decomposition 63
3.1. Stochastic Cutting Plane Method 64
3.2. Asymptotic Analysis of the SCP Algorithm 72
3.2.1. Preliminaries 72
3.2.2. Asymptotic Results for the SCP Method 74
3.3. Subproblem Approximation 81
3.4. A Basic Stochastic Decomposition Algorithm 87
3.5. Bibliographical Notes 95
References 97
4. Stabilizing Stochastic Decomposition 99
4.1. An Algorithm with Incumbent Solutions 101
4.2. A Regularized Master Program Ill
4.3. Bibliographical Notes 120
Appendix: Proof of Theorem 4.4 122
References 129
5. Stopping Rules for Stochastic Decomposition 131
5.1. Termination Based on Asymptotic Properties 133
5.1.1. Identification of a Convergent Subsequence 133
5.1.2. Estimated Objective Value Stability 136
5.2. Termination Based on Error Bound Estimates 139
5.2.1. Statistical Estimation of Error Bounds 140
5.2.2. Error Bound Variability: A Conceptual Procedure .. 142
5.2.3. Error Bound Variability: A Bootstrap Procedure ... 145
5.3. Termination Based on Optimality Conditions 152
5.3.1. Summary of Optimality Conditions 152
ix
5.3.2. Optimality Tests for the Case With Sampling 155
5.4. A Preliminary Test Prior to Termination 158
5.5. A Preliminary Comparison of Termination Criteria 159
5.6. Bibliographical Notes 162
References 164
6. Guidelines for Computer Implementation 165
6.1. Recursive Updates for Cut Formation 167
6.2. Cut Formation and Resampling 174
6.2.1. Forming Cuts 174
6.2.2. Updating Cuts 176
6.2.3. Resampling 178
6.3. Implementation of Statistical Optimality Tests 180
6.4. Bibliographical Notes 182
References 183
7. Illustrative Computational Experiments 185
7.1. Test Problem Characteristics 186
7.2. Performance Measures 188
7.3. Termination Based on Statistical Tests of Optimality ... 190
7.4. Regularized Master Program 194
7.5. Large Scale Implementation 204
7.5.1. STORM 206
7.5.2. SSN 209
7.6. Bibliographical Notes 213
References 214.
Glossary 215
|
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-sort | 3519.7 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV010998215 |
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| indexdate | 2024-07-09T18:02:22Z |
| institution | BVB |
| isbn | 0792338405 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007362543 |
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| physical | XXIII, 220 S.: graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Kluwer |
| record_format | marc |
| series | Nonconvex optimization and its applications |
| series2 | Nonconvex optimization and its applications |
| spelling | Higle, Julia L. Verfasser aut Stochastic decomposition a statistical method for large scale stochastic linear programming by Julia L. Higle and Suvrajeet Sen Dordrecht [u.a.] Kluwer 1996 XXIII, 220 S.: graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nonconvex optimization and its applications 8 Lineaire programmering gtt Programmation stochastique Stochastische programmering gtt Stochastic programming Algorithmus (DE-588)4001183-5 gnd rswk-swf Dekomposition (DE-588)4149030-7 gnd rswk-swf Stochastische Optimierung (DE-588)4057625-5 gnd rswk-swf Stochastische lineare Optimierung (DE-588)4183378-8 gnd rswk-swf Stochastische Optimierung (DE-588)4057625-5 s Algorithmus (DE-588)4001183-5 s DE-604 Stochastische lineare Optimierung (DE-588)4183378-8 s Dekomposition (DE-588)4149030-7 s Sen, Suvrajeet Verfasser aut Nonconvex optimization and its applications 8 (DE-604)BV010085908 8 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007362543&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Higle, Julia L. Sen, Suvrajeet Stochastic decomposition a statistical method for large scale stochastic linear programming Nonconvex optimization and its applications Lineaire programmering gtt Programmation stochastique Stochastische programmering gtt Stochastic programming Algorithmus (DE-588)4001183-5 gnd Dekomposition (DE-588)4149030-7 gnd Stochastische Optimierung (DE-588)4057625-5 gnd Stochastische lineare Optimierung (DE-588)4183378-8 gnd |
| subject_GND | (DE-588)4001183-5 (DE-588)4149030-7 (DE-588)4057625-5 (DE-588)4183378-8 |
| title | Stochastic decomposition a statistical method for large scale stochastic linear programming |
| title_auth | Stochastic decomposition a statistical method for large scale stochastic linear programming |
| title_exact_search | Stochastic decomposition a statistical method for large scale stochastic linear programming |
| title_full | Stochastic decomposition a statistical method for large scale stochastic linear programming by Julia L. Higle and Suvrajeet Sen |
| title_fullStr | Stochastic decomposition a statistical method for large scale stochastic linear programming by Julia L. Higle and Suvrajeet Sen |
| title_full_unstemmed | Stochastic decomposition a statistical method for large scale stochastic linear programming by Julia L. Higle and Suvrajeet Sen |
| title_short | Stochastic decomposition |
| title_sort | stochastic decomposition a statistical method for large scale stochastic linear programming |
| title_sub | a statistical method for large scale stochastic linear programming |
| topic | Lineaire programmering gtt Programmation stochastique Stochastische programmering gtt Stochastic programming Algorithmus (DE-588)4001183-5 gnd Dekomposition (DE-588)4149030-7 gnd Stochastische Optimierung (DE-588)4057625-5 gnd Stochastische lineare Optimierung (DE-588)4183378-8 gnd |
| topic_facet | Lineaire programmering Programmation stochastique Stochastische programmering Stochastic programming Algorithmus Dekomposition Stochastische Optimierung Stochastische lineare Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007362543&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010085908 |
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