{"id":"https://openalex.org/W2023587476","doi":"https://doi.org/10.1137/110825054","title":"A Distance For Multistage Stochastic Optimization Models","display_name":"A Distance For Multistage Stochastic Optimization Models","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2023587476","doi":"https://doi.org/10.1137/110825054","mag":"2023587476"},"language":"en","primary_location":{"id":"doi:10.1137/110825054","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110825054","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/A5002688746","display_name":"Georg Ch. Pflug","orcid":"https://orcid.org/0000-0001-8215-3550"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Georg Ch. Pflug","raw_affiliation_strings":["georg.pflug@univie.ac.at#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"georg.pflug@univie.ac.at#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028943473","display_name":"Alois Pichler","orcid":"https://orcid.org/0000-0001-8876-2429"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alois Pichler","raw_affiliation_strings":["alois.pichler@univie.ac.at#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"alois.pichler@univie.ac.at#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.745,"has_fulltext":false,"cited_by_count":139,"citation_normalized_percentile":{"value":0.98117503,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"22","issue":"1","first_page":"1","last_page":"23"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9909999966621399,"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"}},"topics":[{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9909999966621399,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9801999926567078,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12137","display_name":"Economic theories and models","score":0.9158999919891357,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7408186793327332},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.543646514415741},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5386483669281006},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4969623386859894},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4834359884262085},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.443785697221756},{"id":"https://openalex.org/keywords/stochastic-modelling","display_name":"Stochastic modelling","score":0.4212939441204071},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.418666273355484},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4002176821231842},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.20250141620635986},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11029690504074097},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09264034032821655}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7408186793327332},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.543646514415741},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5386483669281006},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4969623386859894},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4834359884262085},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.443785697221756},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.4212939441204071},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.418666273355484},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4002176821231842},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20250141620635986},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11029690504074097},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09264034032821655}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/110825054","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110825054","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"},{"id":"pmh:oai:https://orca.cardiff.ac.uk:91099","is_oa":false,"landing_page_url":"https://orca.cardiff.ac.uk/91099/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401195","display_name":"ORCA Online Research @Cardiff (Cardiff University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79510175","host_organization_name":"Cardiff University","host_organization_lineage":["https://openalex.org/I79510175"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:pure.iiasa.ac.at:9970","is_oa":false,"landing_page_url":"http://pure.iiasa.ac.at/id/eprint/9970/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401423","display_name":"IIASA PURE (International Institute of Applied Systems Analysis)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1317774081","host_organization_name":"International Institute for Applied Systems Analysis","host_organization_lineage":["https://openalex.org/I1317774081"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W144179185","https://openalex.org/W385466589","https://openalex.org/W1485598997","https://openalex.org/W1509154951","https://openalex.org/W1522579744","https://openalex.org/W1601076586","https://openalex.org/W1971451499","https://openalex.org/W1985077192","https://openalex.org/W1996289149","https://openalex.org/W1996936277","https://openalex.org/W2010525458","https://openalex.org/W2013951488","https://openalex.org/W2014528122","https://openalex.org/W2016315504","https://openalex.org/W2027818174","https://openalex.org/W2028712970","https://openalex.org/W2060013459","https://openalex.org/W2072633759","https://openalex.org/W2076355050","https://openalex.org/W2087682750","https://openalex.org/W2099332713","https://openalex.org/W2119407575","https://openalex.org/W2127837929","https://openalex.org/W2132883347","https://openalex.org/W2155913608","https://openalex.org/W2169071224","https://openalex.org/W2254463431","https://openalex.org/W2506539929","https://openalex.org/W3009330671"],"related_works":["https://openalex.org/W3185235544","https://openalex.org/W2911623553","https://openalex.org/W4297791327","https://openalex.org/W2897842840","https://openalex.org/W2397777611","https://openalex.org/W1502031429","https://openalex.org/W2417585376","https://openalex.org/W1994157709","https://openalex.org/W4294336468","https://openalex.org/W4312526853"],"abstract_inverted_index":{"We":[0,74],"describe":[1],"multistage":[2,99],"stochastic":[3,71,100,114,159],"programs":[4],"in":[5,31,84,108,137],"a":[6,15,64,143],"purely":[7],"in-distribution":[8],"setting,":[9],"i.e.,":[10],"without":[11],"any":[12],"reference":[13],"to":[14,48,62,140],"concrete":[16],"probability":[17],"space.":[18],"The":[19,51,86,152],"concept":[20],"is":[21,57,134,150,154,177,198,204],"based":[22],"on":[23],"the":[24,35,41,67,91,94,109,113,120,129,147,168,182,187,190],"notion":[25],"of":[26,66,77,93,97,112,123,189],"nested":[27,52,110,121,148,169],"distributions,":[28],"which":[29,45,102,133],"encompass":[30],"one":[32],"mathematical":[33],"object":[34],"scenario":[36,164,175,191,201],"values":[37,96],"as":[38,40],"well":[39,178],"information":[42],"structure":[43],"under":[44],"decisions":[46],"have":[47],"be":[49,63,117],"made.":[50],"distance":[53,69,79,122,149,170,197],"between":[54,171],"these":[55,124],"distributions":[56],"introduced":[58],"and":[59,80,105,161,174,180],"turns":[60],"out":[61],"generalization":[65],"Wasserstein":[68],"for":[70,146,157,162,185],"two-stage":[72,138],"problems.":[73],"give":[75],"characterizations":[76],"this":[78],"show":[81],"its":[82],"usefulness":[83],"examples.":[85],"main":[87],"result":[88],"states":[89],"that":[90],"difference":[92],"optimal":[95],"two":[98],"programs,":[101],"are":[103],"Lipschitz":[104],"differ":[106],"only":[107,136],"distribution":[111],"parameters,":[115],"can":[116],"bounded":[118],"by":[119],"distributions.":[125],"This":[126],"theorem":[127],"generalizes":[128],"well-known":[130],"Kantorovich\u2013Rubinstein":[131],"theorem,":[132],"applicable":[135,155],"situations,":[139],"multistage.":[141],"Moreover,":[142],"dual":[144],"characterization":[145],"established.":[151],"setup":[153],"both":[156],"general":[158,172],"processes":[160,173],"finite":[163],"trees.":[165],"In":[166],"particular,":[167],"trees":[176],"defined":[179],"becomes":[181],"important":[183],"tool":[184],"judging":[186],"quality":[188],"tree":[192,202],"generation.":[193],"Minimizing\u2014at":[194],"least":[195],"heuristically\u2014this":[196],"what":[199],"good":[200],"generation":[203],"all":[205],"about.":[206]},"counts_by_year":[{"year":2026,"cited_by_count":10},{"year":2025,"cited_by_count":15},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}