Stochastic linear programming: models, theory, and computation
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2011
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | International series in operations research & management science
156 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XX, 426 S. graph. Darst. |
| ISBN: | 9781441977281 9781441977298 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text |
Titel: Stochastic linear programming
Autor: Kall, Peter
Jahr: 2011
Contents
Preface.vii
Notations.xvii
1 Basics.I
1.1 Introduction.1
Exercises .6
1.2 Linear Programming Prerequisites .7
1.2.1 Algebraic concepts and properties.7
1.2.2 Geometric interpretation.10
1.2.3 Duality statements.12
1.2.4 The Simplex method.16
1.2.5 The dual Simplex method.20
Exercises .22
1.2.6 Dual decomposition method.23
1.2.7 Nested decomposition.31
1.2.8 Regularized decomposition.46
1.2.9 Interior Point Methods.48
Exercises .53
1.3 Nonlinear Programming Prerequisites .54
1.3.1 Optimality Conditions.57
1.3.2 Solution methods.59
Cutting Planes: Outer Linearization (Kelley).61
Cutting Planes: Outer Linearization (Veinott).63
Cutting Planes: Outer Linearization (Zoutendijk).65
A Central Cutting Plane Method (Elzinga-Moore) .66
Exercises .69
2 Single-stage SLP models.71
2.1 Introduction.71
Exercises .87
2.2 Models involving probability functions .87
2.2.1 Basic properties .91
2.2.2 Finite discrete distribution.93. -
2.2.3 Separate probability functions. _95
Only the right-hand-side is stochastic.97
Multivariate normal distribution.98
Stable distributions.106
A distribution-free approach.111
2.2.4 The independent case.113
2.2.3 Joint constraints: random right-hand-side .115
Generalized-concave probability measures.116
Generalized-concave distribution functions.125
Maximizing joint probability functions.128
2.2.6 Joint constraints: random technology matrix.129
2.2.7 Summary on the convex programming subclasses.134
Exercises .136
2.3 Quantité functions, Value at Risk .137
2.4 Models based on expectation.140
2.4.1 Integrated chance constraints .142
Separate integrated probability functions.142
Joint integrated probability functions.147
2.4.2 A model involving conditional expectation.151
2.4.3 Conditional Value at Risk.152
Exercises .158
2.5 Models built with deviation measures.159
2.5.1 Quadratic deviation .160
2.5.2 Absolute deviation.163
2.5.3 Quadratic semi-deviation.167
2.5.4 Absolute semi-deviation.170
Exercises .171
2.6 Modeling risk and opportunity.171
2.7 Risk measures.173
2.7.1 Risk measures in finance.175
2.7.2 Properties of risk measures.177
2.7.3 Portfolio optimization models.1S1
2.7.4 Optimizing performance.183
Exercises .188
SLP models with recourse.191
3.1 The general multi-stage SLP. . 191
3.2 The two-stage SLP: Properties and solution appraoches.196
3.2.1 The complete fixed recourse problem (CFR) .198
3.2.1.1 CFR. Direct bounds for the expected recourse 2(x)207
3.2.1.2 CFR: Moment problems and bounds for 2(x) . 209
3.2.1.3 CFR: Approximation by successive discretization .218
DAPPROX: Approximating CFR solutions.223
Exercises .224
3.2.2 The simple recourse case.226
3.2.2.1 The standard simple recourse problem (SSR).227
3.2.2.2 SSR: Approximation by successive discretization . 232
SRAPPROX: Approximating SSR solutions.235
3.2.2.3 The multiple simple recourse problem.237
3.2.2.4 The generalized simple recourse problem (GSR). 244
GSR-CUT: Solving GSR by successive cuts.247
Exercises .249
3.2.3 CVaR and recourse problems.250
3.2.4 Some characteristic values for two-stage SLP's.255
3.3 The multi-stage SEP.260
3.3.1 MSLP with finite discrete distributions.261
3.3.2 MSLP with non-discrete distributions.266
4 Algorithms.285
4.1 Introduction.285
4.2 Single-stage models with separate probability functions.285
4.2.1 A guide to available software.287
4.3 Single-stage models with joint probability functions.288
4.3.1 Numerical considerations.289
4.3.2 Cutting plane methods.293
4.3.3 Other algorithms.295
4.3.4 Bounds for the probability distribution function.296
4.3.5 Computing probability distribution functions.303
A Monte-Carlo approach with antithetic variâtes.304
A Monte-Carlo approach based on probability bounds.306
4.3.6 Finite discrete distributions.309
4.3.7 A guide to available software.311
SEP problems with logconcave distribution functions.311
Evaluating probability distribution functions .311
SEP problems with finite discrete distributions.312
Exercises .312
4.4 Single-stage models based on expectation.313
4.4.1 Solving equivalent LP's.313
4.4.2 Dual decomposition revisited.314
4.4.3 Models with separate integrated probability functions.318
4.4.4 Models involving CVaR.320
4.4.5 Models with joint integrated probability functions.322
4.4.6 A guide to available software.324
Models with separate integrated probability functions.324
Models with joint integrated probability functions.325
Models involving CVaR.325
Exercises .325
4.5 Single-stage models involving VaR.-325
4.6 Single-stage models with deviation measures.-326
4.6.1 A guide to available software.327
4.7 Two-stage recourse models.-327
4.7.1 Decomposition methods .328
4.7.2 Successive discrete approximation methods.329
Computing the Jensen lower bound.330
Computing the E-M upper bound for an interval.331
Computing the bounds for a partition.333
The successive discrete approximation method .337
Implementation.341
Simple recourse.346
Other successive discrete approximation algorithms.350
4.7.3 Stochastic algorithms.351
Sample average approximation (SAA).351
Stochastic decomposition .357
Other stochastic algorithms.360
4.7.4 Simple recourse models.361
4.7.5 A guide to available software.361
Exercises .363
4.8 Multistage recourse models.364
4.8.1 Finite discrete distribution.364
4.8.2 Scenario generation.366
Bundle-based sampling.368
A moment-matching heuristics .369
4.8.3 A guide to available software.375
4.9 Modeling systems for SEP.375
4.9.1 Modeling systems for SLP .376
4.9.2 SLP-IOR.377
General issues.378
Analyze tools and workbench facilities.379
Transformations.380
Scenario generation.380
The solver interface.380
System requirements and availability.382
References.383
Exercises: Hints for answers 405
Index 421 |
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| edition | 2. ed. |
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| physical | XX, 426 S. graph. Darst. |
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| series2 | International series in operations research & management science |
| spelling | Kall, Peter 1939-2016 (DE-588)1089936869 aut Stochastic linear programming models, theory, and computation Peter Kall ; János Mayer 2. ed. New York [u.a.] Springer 2011 XX, 426 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series in operations research & management science 156 Linear programming Stochastic processes Stochastische lineare Optimierung (DE-588)4183378-8 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Stochastische Optimierung (DE-588)4057625-5 gnd rswk-swf Stochastische Optimierung (DE-588)4057625-5 s DE-604 Lineare Optimierung (DE-588)4035816-1 s Stochastische lineare Optimierung (DE-588)4183378-8 s Mayer, János (DE-588)170816982 aut Erscheint auch als Online-Ausgabe Stochastic Linear Programming International series in operations research & management science 156 (DE-604)BV011630976 156 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3523285&prov=M&dok%5Fvar=1&dok%5Fext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024462118&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kall, Peter 1939-2016 Mayer, János Stochastic linear programming models, theory, and computation International series in operations research & management science Linear programming Stochastic processes Stochastische lineare Optimierung (DE-588)4183378-8 gnd Lineare Optimierung (DE-588)4035816-1 gnd Stochastische Optimierung (DE-588)4057625-5 gnd |
| subject_GND | (DE-588)4183378-8 (DE-588)4035816-1 (DE-588)4057625-5 |
| title | Stochastic linear programming models, theory, and computation |
| title_auth | Stochastic linear programming models, theory, and computation |
| title_exact_search | Stochastic linear programming models, theory, and computation |
| title_full | Stochastic linear programming models, theory, and computation Peter Kall ; János Mayer |
| title_fullStr | Stochastic linear programming models, theory, and computation Peter Kall ; János Mayer |
| title_full_unstemmed | Stochastic linear programming models, theory, and computation Peter Kall ; János Mayer |
| title_short | Stochastic linear programming |
| title_sort | stochastic linear programming models theory and computation |
| title_sub | models, theory, and computation |
| topic | Linear programming Stochastic processes Stochastische lineare Optimierung (DE-588)4183378-8 gnd Lineare Optimierung (DE-588)4035816-1 gnd Stochastische Optimierung (DE-588)4057625-5 gnd |
| topic_facet | Linear programming Stochastic processes Stochastische lineare Optimierung Lineare Optimierung Stochastische Optimierung |
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| volume_link | (DE-604)BV011630976 |
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