Formulating Two-Stage Stochastic Programs for Interior Point Methods
This paper describes an approach for modeling two-stage stochastic programs that yields a form suitable for interior point algorithms. A staircase constraint structure is created by replacing first stage variables with sparse "split variables" in conjunction with side-constraints. Dense co...
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| Veröffentlicht in: | Operations research 1991-09, Vol.39 (5), p.757-770 |
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| creator | Lustig, Irvin J Mulvey, John M Carpenter, Tamra J |
| description | This paper describes an approach for modeling two-stage stochastic programs that yields a form suitable for interior point algorithms. A staircase constraint structure is created by replacing first stage variables with sparse "split variables" in conjunction with side-constraints. Dense columns are thereby eliminated. The resulting model is larger than traditional stochastic programs, but computational savings are substantial—over a tenfold improvement for the problems tested. A series of experiments with stochastic networks drawn from financial planning demonstrates the attained efficiencies. Comparisons with MINOS and the dual block angular stochastic programming model are provided as benchmarks. The split variable approach is applicable to general two-stage stochastic programs and other dual block angular models. |
| doi_str_mv | 10.1287/opre.39.5.757 |
| format | Article |
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A staircase constraint structure is created by replacing first stage variables with sparse "split variables" in conjunction with side-constraints. Dense columns are thereby eliminated. The resulting model is larger than traditional stochastic programs, but computational savings are substantial—over a tenfold improvement for the problems tested. A series of experiments with stochastic networks drawn from financial planning demonstrates the attained efficiencies. Comparisons with MINOS and the dual block angular stochastic programming model are provided as benchmarks. The split variable approach is applicable to general two-stage stochastic programs and other dual block angular models.</description><identifier>ISSN: 0030-364X</identifier><identifier>EISSN: 1526-5463</identifier><identifier>DOI: 10.1287/opre.39.5.757</identifier><identifier>CODEN: OPREAI</identifier><language>eng</language><publisher>Linthicum, MD: INFORMS</publisher><subject>Aggregation ; Algorithms ; Applied sciences ; Comparative studies ; Determinism ; Equations ; Exact sciences and technology ; Interior points ; Linear programming ; linear: techniques for stochastic linear programs ; Mathematical models ; Mathematical programming ; Objective functions ; Operational research and scientific management ; Operational research. Management science ; Operations research ; programming ; Staircases ; Statistical analysis ; Stochastic models ; stochastic: solution by interior point methods ; Theory</subject><ispartof>Operations research, 1991-09, Vol.39 (5), p.757-770</ispartof><rights>Copyright 1991 The Operations Research Society of America</rights><rights>1992 INIST-CNRS</rights><rights>Copyright Institute for Operations Research and the Management Sciences Sep/Oct 1991</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2546-a953148690ecf506dc7ffd5e4d00b886c55ffc6e6fbb95e4fce1fdfbc7bf26c73</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/171205$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://pubsonline.informs.org/doi/full/10.1287/opre.39.5.757$$EHTML$$P50$$Ginforms$$H</linktohtml><link.rule.ids>314,778,782,801,3681,27856,27911,27912,58004,58237,62601</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=5273522$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Lustig, Irvin J</creatorcontrib><creatorcontrib>Mulvey, John M</creatorcontrib><creatorcontrib>Carpenter, Tamra J</creatorcontrib><title>Formulating Two-Stage Stochastic Programs for Interior Point Methods</title><title>Operations research</title><description>This paper describes an approach for modeling two-stage stochastic programs that yields a form suitable for interior point algorithms. A staircase constraint structure is created by replacing first stage variables with sparse "split variables" in conjunction with side-constraints. Dense columns are thereby eliminated. The resulting model is larger than traditional stochastic programs, but computational savings are substantial—over a tenfold improvement for the problems tested. A series of experiments with stochastic networks drawn from financial planning demonstrates the attained efficiencies. Comparisons with MINOS and the dual block angular stochastic programming model are provided as benchmarks. The split variable approach is applicable to general two-stage stochastic programs and other dual block angular models.</description><subject>Aggregation</subject><subject>Algorithms</subject><subject>Applied sciences</subject><subject>Comparative studies</subject><subject>Determinism</subject><subject>Equations</subject><subject>Exact sciences and technology</subject><subject>Interior points</subject><subject>Linear programming</subject><subject>linear: techniques for stochastic linear programs</subject><subject>Mathematical models</subject><subject>Mathematical programming</subject><subject>Objective functions</subject><subject>Operational research and scientific management</subject><subject>Operational research. 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| ispartof | Operations research, 1991-09, Vol.39 (5), p.757-770 |
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| source | INFORMS PubsOnLine; Periodicals Index Online; EBSCOhost Business Source Complete; Jstor Complete Legacy |
| subjects | Aggregation Algorithms Applied sciences Comparative studies Determinism Equations Exact sciences and technology Interior points Linear programming linear: techniques for stochastic linear programs Mathematical models Mathematical programming Objective functions Operational research and scientific management Operational research. Management science Operations research programming Staircases Statistical analysis Stochastic models stochastic: solution by interior point methods Theory |
| title | Formulating Two-Stage Stochastic Programs for Interior Point Methods |
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