{"id":"https://openalex.org/W2012436468","doi":"https://doi.org/10.1137/0804048","title":"Parallel Factorization of Structured Matrices Arising in Stochastic Programming","display_name":"Parallel Factorization of Structured Matrices Arising in Stochastic Programming","publication_year":1994,"publication_date":"1994-11-01","ids":{"openalex":"https://openalex.org/W2012436468","doi":"https://doi.org/10.1137/0804048","mag":"2012436468"},"language":"en","primary_location":{"id":"doi:10.1137/0804048","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0804048","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041552096","display_name":"Elizabeth R. Jessup","orcid":"https://orcid.org/0000-0002-7740-9985"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Elizabeth R. Jessup","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028806797","display_name":"Dafeng Yang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dafeng Yang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5060322411","display_name":"Stavros A. Zenios","orcid":"https://orcid.org/0000-0001-7576-4898"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stavros A. Zenios","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.5214,"has_fulltext":false,"cited_by_count":60,"citation_normalized_percentile":{"value":0.96943649,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"4","issue":"4","first_page":"833","last_page":"846"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9882000088691711,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9882000088691711,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9865000247955322,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9853000044822693,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.681182324886322},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6557148098945618},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.6413043141365051},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5904176235198975},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.5731052160263062},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.49514999985694885},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4896738827228546},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.4810386002063751},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.46575433015823364},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.46261316537857056},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45086273550987244},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37448012828826904},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3554925322532654},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.33166956901550293},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3025808334350586},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.22243216633796692}],"concepts":[{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.681182324886322},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6557148098945618},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.6413043141365051},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5904176235198975},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.5731052160263062},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.49514999985694885},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4896738827228546},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.4810386002063751},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.46575433015823364},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.46261316537857056},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45086273550987244},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37448012828826904},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3554925322532654},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.33166956901550293},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3025808334350586},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22243216633796692},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0804048","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0804048","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1965230003","https://openalex.org/W1969007958","https://openalex.org/W1969197658","https://openalex.org/W1973615364","https://openalex.org/W2022360658","https://openalex.org/W2022985590","https://openalex.org/W2094542090","https://openalex.org/W2116337907","https://openalex.org/W2138492203","https://openalex.org/W2145786890","https://openalex.org/W2603223509","https://openalex.org/W4244968939","https://openalex.org/W4246699152"],"related_works":["https://openalex.org/W2965106131","https://openalex.org/W2114808974","https://openalex.org/W2094757704","https://openalex.org/W25030584","https://openalex.org/W29231041","https://openalex.org/W2610104823","https://openalex.org/W1970997620","https://openalex.org/W2092044038","https://openalex.org/W2144582354","https://openalex.org/W2074889170"],"abstract_inverted_index":{"Solving":[0],"the":[1,14,20,48,53,68,77,117,120],"deterministic":[2,136],"equivalent":[3,137],"formulation":[4],"of":[5,16,19,55,70,74,79,119],"two-stage":[6],"stochastic":[7,126],"programs":[8,127,139],"using":[9,47],"interior":[10],"point":[11],"algorithms":[12,82],"requires":[13,67],"solution":[15,69,118],"linear":[17,121,138],"systems":[18,73,122],"form\\[":[21],"\\left(":[22],"AD^2":[23],"A^\\top":[24],"\\right)":[25],"dy":[26],"=":[27],"b":[28],".":[29],"\\]":[30],"The":[31],"constraint":[32],"matrix":[33,44],"A":[34],"has":[35],"a":[36,42,89,109],"dual,":[37],"block-angular":[38],"structure.":[39],"We":[40],"develop":[41],"parallel":[43,90],"factorization":[45],"procedure":[46,66],"Sherman\u2013Morrison\u2013Woodbury":[49],"formula,":[50],"based":[51],"on":[52,103],"work":[54],"Birge":[56],"and":[57,83,108,145],"Qi":[58],"[Management":[59],"Sci.,":[60],"34":[61],"(1988),":[62],"pp.":[63],"1472\u20131479].":[64],"This":[65],"smaller,":[71],"independent":[72],"equations.":[75],"With":[76],"use":[78],"optimal":[80],"communication":[81],"careful":[84],"attention":[85],"to":[86,130,135,142],"data":[87],"layout":[88],"implementation":[91],"is":[92,101],"obtained":[93],"that":[94],"achieves":[95],"near":[96],"perfect":[97],"speedup.":[98],"Scalable":[99],"performance":[100],"observed":[102],"an":[104],"Intel":[105],"iPSC/860":[106],"hypercube":[107],"Connection":[110],"Machine":[111],"CM\u20135.":[112],"Results":[113],"are":[114],"reported":[115],"with":[116,128,140],"arising":[123],"when":[124],"solving":[125],"up":[129,141],"98,304":[131],"scenarios,":[132],"which":[133],"correspond":[134],"1,966,090":[143],"constraints":[144],"13,762,630":[146],"variables.":[147]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}