Stochastic programming:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester [u.a.]
Wiley
1995
|
| Edition: | Reprinted |
| Series: | Wiley-Interscience series in systems and optimization
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XII, 307 S. graph. Darst. |
| ISBN: | 0471951080 0471951587 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | STOCHASTIC PROGRAMMING PETER KALL INSTITUTE FOV OPERATIONS RESEARCH AND
MATHEMATICAL METHODS OF ECONOMICS UNIVERSITY OF ZUERICH S WITZER] AND
STEIN W. WALLACE DEPARTMENT OF MANAGERIA] ECONOMICS AND OPERATIONS
RESEARCH NORWEGIAN INSTITUTE OF TECHNOLOGY UNIVERSITY OF TRONDHEIM
NORWAY JOHN WILEY & SONS CHICHESTER * NEW YORK * BRISBANE TORONTO *
SINGAPORE CONTENTS PREFACE IX 1 BASIC CONCEPTS 1 1.1 PRELIMINARIES 1 1.2
AN ILLUSTRATIVE EXAMPLE 4 1.3 STOCHASTIC PROGRAMS: GENERAL FORMULATION
15 1.3.1 MEASURES AND INTEGRALS 16 1.3.2 DETERMINISTIC EQUIVALENTS 25
1.4 PROPERTIES OF RECOURSE PROBLEMS 31 FL.5 PROPERTIES OF PROBABILISTIC
CONSTRAINTS 41 1.6 LINEAR PROGRAMMING 48 1.6.1 THE FEASIBLE SET AND
SOLVABILITY 49 1.6.2 THE SIMPLEX ALGORITHM 59 1.6.3 DUALITY STATEMENTS
64 1.6.4 A DUAL DECOMPOSITION METHOD 70 1.7 NONLINEAR PROGRAMMING 75
1.7.1 THE KUHN-TUCKER CONDITIONS 77 1.7.2 SOLUTION TECHNIQUES 84 1.7.2.1
CUTTING-PLANE METHODS 84 1.7.2.2 DESCENT METHODS 88 1.7.2.3 PENALTY
METHODS 91 1.7.2.4 LAGRANGIAN METHODS 93 1.8 BIBLIOGRAPHICAL NOTES 97
EXERCISES 99 REFERENCES 100 2 DYNAMIC SYSTEMS 105 2.1 THE BELLMAN
PRINCIPLE 105 2.2 DYNAMIC PROGRAMMING 112 2.3 DETERMINISTIC DECISION
TREES 116 2.4 STOCHASTIC DECISION TREES 119 VI CONTENTS 2.5 STOCHASTIC
DYNAMIC PROGRAMMING 124 2.6 SCENARIO AGGREGATION 129 2.6.1 APPROXIMATE
SCENARIO SOLUTIONS 136 2.7 THE VALUE OF USING A STOCHASTIC MODEL 137
2.7.1 COMPARING THE DETERMINISTIC AND STOCHASTIC OBJECTIVE VALUES 137
2.7.2 DETERMINISTIC SOLUTIONS IN THE EVENT TREE 138 2.7.3 EXPECTED VALUE
OF PERFECT INFORMATION 140 2.8 BIBLIOGRAPHICAL NOTES 143 EXERCISES 143
REFERENCES 144 3 RECOURSE PROBLEMS 147 3.1 OUTLINE OF STRUCTURE 147 3.2
THE L-SHAPED DECOMPOSITION METHOD 149 3.2.1 FEASIBILITY 149 3.2.2
OPTIMALITY 155 3.3 REGULARIZED DECOMPOSITION 161 3.4 BOUNDS 165 3.4.1
THE JENSEN LOWER BOUND 167 3.4.2 EDMUNDSON-MADANSKY UPPER BOUND 168
3.4.3 COMBINATIONS 172 3.4.4 A PIECEWISE LINEAR UPPER BOUND 173 3.5
APPROXIMATIONS 178 3.5.1 REFINEMENTS OF THE WAIT-AND-SEE SOLUTION 178
3.5.2 USING THE L-SHAPED METHOD WITHIN APPROXIMATION SCHEINES 189 3.5.3
WHAT IS A GOOD PARTITION? 191 3.6 SIMPLE RECOURSE 193 3.7 INTEGER FIRST
STAGE 197 3.7.1 INITIALIZATION 203 3.7.2 FEASIBILITY CUTS 203 3.7.3
OPTIMALITY CUTS 203 3.7.4 STOPPING CRITERIA 203 3.8 STOCHASTIC
DECOMPOSITION 205 3.9 STOCHASTIC QUASI-GRADIENT METHODS 213 3.10 SOLVING
MANY SIMILAR LINEAR PROGRAMS 218 3.10.1 RANDOMNESS IN THE OBJECTIVE 221
3.11 BIBLIOGRAPHICAL NOTES 221 EXERCISES 223 REFERENCES 225 4
PROBABILISTIC CONSTRAINTS 231 CONTENTS VII 4.1 JOINT CHANCE CONSTRAINED
PROBLEMS 233 4.2 SEPARATE CHANCE CONSTRAINTS 235 4.3 BOUNDING
DISTRIBUTION FUNCTIONS 237 4.4 BIBLIOGRAPHICAL NOTES 245 EXERCISES 246
REFERENCES 246 5 PREPROCESSING 249 5.1 PROBLEM REDUCTION 249 5.1.1
FINDING A FRAME 250 5.1.2 REMOVING UNNECESSARY COLUMNS 251 5.1.3
REMOVING UNNECESSARY ROWS 252 5.2 FEASIBILITY IN LINEAR PROGRAMS 253
5.2.1 A SMALL EXAMPLE 260 5.3 REDUCING THE COMPLEXITY OF FEASIBILITY
TESTS 261 5.4 BIBLIOGRAPHICAL NOTES 262 EXERCISES 262 REFERENCES 263 6
NETWORK PROBLEMS 265 6.1 TERMINOLOGY 266 6.2 FEASIBILITY IN NETWORKS 268
6.2.1 COMPARING THE LP AND NETWORK CASES 276 6.3 GENERATING RELATIVELY
COMPLETE RECOURSE 277 6.4 AN INVESTMENT EXAMPLE 279 6.5 BOUNDS 283 6.5.1
PIECEWISE LINEAR UPPER BOUNDS 284 6.6 PROJECT SCHEDULING 291 6.6.1 PERT
AS A DECISION PROBLEM 292 6.6.2 INTRODUCTION OF RANDOMNESS 292 6.6.3
BOUNDS ON THE EXPECTED PROJECT DURATION 294 6.6.3.1 SERIES REDUCTIONS
294 6.6.3.2 PARALLEL REDUCTIONS 294 6.6.3.3 DISREGARDING PATH
DEPENDENCES 294 6.6.3.4 ARE DUPLICATIONS 295 6.6.3.5 USING JENSEN S
INEQUALITY 296 6.7 BIBLIOGRAPHICAL NOTES 296 EXERCISES 297 REFERENCES
299 INDEX 303
|
| adam_txt |
STOCHASTIC PROGRAMMING PETER KALL INSTITUTE FOV OPERATIONS RESEARCH AND
MATHEMATICAL METHODS OF ECONOMICS UNIVERSITY OF ZUERICH S WITZER] AND
STEIN W. WALLACE DEPARTMENT OF MANAGERIA] ECONOMICS AND OPERATIONS
RESEARCH NORWEGIAN INSTITUTE OF TECHNOLOGY UNIVERSITY OF TRONDHEIM
NORWAY JOHN WILEY & SONS CHICHESTER * NEW YORK * BRISBANE ' TORONTO *
SINGAPORE CONTENTS PREFACE IX 1 BASIC CONCEPTS 1 1.1 PRELIMINARIES 1 1.2
AN ILLUSTRATIVE EXAMPLE 4 1.3 STOCHASTIC PROGRAMS: GENERAL FORMULATION
15 1.3.1 MEASURES AND INTEGRALS 16 1.3.2 DETERMINISTIC EQUIVALENTS 25
1.4 PROPERTIES OF RECOURSE PROBLEMS 31 FL.5 PROPERTIES OF PROBABILISTIC
CONSTRAINTS 41 1.6 LINEAR PROGRAMMING 48 1.6.1 THE FEASIBLE SET AND
SOLVABILITY 49 1.6.2 THE SIMPLEX ALGORITHM 59 1.6.3 DUALITY STATEMENTS
64 1.6.4 A DUAL DECOMPOSITION METHOD 70 1.7 NONLINEAR PROGRAMMING 75
1.7.1 THE KUHN-TUCKER CONDITIONS 77 1.7.2 SOLUTION TECHNIQUES 84 1.7.2.1
CUTTING-PLANE METHODS 84 1.7.2.2 DESCENT METHODS 88 1.7.2.3 PENALTY
METHODS 91 1.7.2.4 LAGRANGIAN METHODS 93 1.8 BIBLIOGRAPHICAL NOTES 97
EXERCISES 99 REFERENCES 100 2 DYNAMIC SYSTEMS 105 2.1 THE BELLMAN
PRINCIPLE 105 2.2 DYNAMIC PROGRAMMING 112 2.3 DETERMINISTIC DECISION
TREES 116 2.4 STOCHASTIC DECISION TREES 119 VI CONTENTS 2.5 STOCHASTIC
DYNAMIC PROGRAMMING 124 2.6 SCENARIO AGGREGATION 129 2.6.1 APPROXIMATE
SCENARIO SOLUTIONS 136 2.7 THE VALUE OF USING A STOCHASTIC MODEL 137
2.7.1 COMPARING THE DETERMINISTIC AND STOCHASTIC OBJECTIVE VALUES 137
2.7.2 DETERMINISTIC SOLUTIONS IN THE EVENT TREE 138 2.7.3 EXPECTED VALUE
OF PERFECT INFORMATION 140 2.8 BIBLIOGRAPHICAL NOTES 143 EXERCISES 143
REFERENCES 144 3 RECOURSE PROBLEMS 147 3.1 OUTLINE OF STRUCTURE 147 3.2
THE L-SHAPED DECOMPOSITION METHOD 149 3.2.1 FEASIBILITY 149 3.2.2
OPTIMALITY 155 3.3 REGULARIZED DECOMPOSITION 161 3.4 BOUNDS 165 3.4.1
THE JENSEN LOWER BOUND 167 3.4.2 EDMUNDSON-MADANSKY UPPER BOUND 168
3.4.3 COMBINATIONS 172 3.4.4 A PIECEWISE LINEAR UPPER BOUND 173 3.5
APPROXIMATIONS 178 3.5.1 REFINEMENTS OF THE "WAIT-AND-SEE"SOLUTION 178
3.5.2 USING THE L-SHAPED METHOD WITHIN APPROXIMATION SCHEINES 189 3.5.3
WHAT IS A GOOD PARTITION? 191 3.6 SIMPLE RECOURSE 193 3.7 INTEGER FIRST
STAGE 197 3.7.1 INITIALIZATION 203 3.7.2 FEASIBILITY CUTS 203 3.7.3
OPTIMALITY CUTS 203 3.7.4 STOPPING CRITERIA 203 3.8 STOCHASTIC
DECOMPOSITION 205 3.9 STOCHASTIC QUASI-GRADIENT METHODS 213 3.10 SOLVING
MANY SIMILAR LINEAR PROGRAMS 218 3.10.1 RANDOMNESS IN THE OBJECTIVE 221
3.11 BIBLIOGRAPHICAL NOTES 221 EXERCISES 223 REFERENCES 225 4
PROBABILISTIC CONSTRAINTS 231 CONTENTS VII 4.1 JOINT CHANCE CONSTRAINED
PROBLEMS 233 4.2 SEPARATE CHANCE CONSTRAINTS 235 4.3 BOUNDING
DISTRIBUTION FUNCTIONS 237 4.4 BIBLIOGRAPHICAL NOTES 245 EXERCISES 246
REFERENCES 246 5 PREPROCESSING 249 5.1 PROBLEM REDUCTION 249 5.1.1
FINDING A FRAME 250 5.1.2 REMOVING UNNECESSARY COLUMNS 251 5.1.3
REMOVING UNNECESSARY ROWS 252 5.2 FEASIBILITY IN LINEAR PROGRAMS 253
5.2.1 A SMALL EXAMPLE 260 5.3 REDUCING THE COMPLEXITY OF FEASIBILITY
TESTS 261 5.4 BIBLIOGRAPHICAL NOTES 262 EXERCISES 262 REFERENCES 263 6
NETWORK PROBLEMS 265 6.1 TERMINOLOGY 266 6.2 FEASIBILITY IN NETWORKS 268
6.2.1 COMPARING THE LP AND NETWORK CASES 276 6.3 GENERATING RELATIVELY
COMPLETE RECOURSE 277 6.4 AN INVESTMENT EXAMPLE 279 6.5 BOUNDS 283 6.5.1
PIECEWISE LINEAR UPPER BOUNDS 284 6.6 PROJECT SCHEDULING 291 6.6.1 PERT
AS A DECISION PROBLEM 292 6.6.2 INTRODUCTION OF RANDOMNESS 292 6.6.3
BOUNDS ON THE EXPECTED PROJECT DURATION 294 6.6.3.1 SERIES REDUCTIONS
294 6.6.3.2 PARALLEL REDUCTIONS 294 6.6.3.3 DISREGARDING PATH
DEPENDENCES 294 6.6.3.4 ARE DUPLICATIONS 295 6.6.3.5 USING JENSEN'S
INEQUALITY 296 6.7 BIBLIOGRAPHICAL NOTES 296 EXERCISES 297 REFERENCES
299 INDEX 303 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T16:06:16Z |
| indexdate | 2024-07-09T20:47:38Z |
| institution | BVB |
| isbn | 0471951080 0471951587 |
| language | English |
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| physical | XII, 307 S. graph. Darst. |
| publishDate | 1995 |
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| publisher | Wiley |
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| spelling | Kall, Peter Verfasser aut Stochastic programming Peter Kall ; Stein W. Wallace Reprinted Chichester [u.a.] Wiley 1995 XII, 307 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley-Interscience series in systems and optimization Literaturangaben Stochastische Optimierung Stochastic programming Stochastische Optimierung (DE-588)4057625-5 gnd rswk-swf Stochastische Optimierung (DE-588)4057625-5 s DE-604 Wallace, Stein W. 1956- Verfasser (DE-588)112839320 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015145163&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kall, Peter Wallace, Stein W. 1956- Stochastic programming Stochastische Optimierung Stochastic programming Stochastische Optimierung (DE-588)4057625-5 gnd |
| subject_GND | (DE-588)4057625-5 |
| title | Stochastic programming |
| title_auth | Stochastic programming |
| title_exact_search | Stochastic programming |
| title_exact_search_txtP | Stochastic programming |
| title_full | Stochastic programming Peter Kall ; Stein W. Wallace |
| title_fullStr | Stochastic programming Peter Kall ; Stein W. Wallace |
| title_full_unstemmed | Stochastic programming Peter Kall ; Stein W. Wallace |
| title_short | Stochastic programming |
| title_sort | stochastic programming |
| topic | Stochastische Optimierung Stochastic programming Stochastische Optimierung (DE-588)4057625-5 gnd |
| topic_facet | Stochastische Optimierung Stochastic programming |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015145163&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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