{"id":"https://openalex.org/W2914903271","doi":"https://doi.org/10.1137/17m1140601","title":"Guaranteed Bounds for General Nondiscrete Multistage Risk-Averse Stochastic Optimization Programs","display_name":"Guaranteed Bounds for General Nondiscrete Multistage Risk-Averse Stochastic Optimization Programs","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2914903271","doi":"https://doi.org/10.1137/17m1140601","mag":"2914903271"},"language":"en","primary_location":{"id":"doi:10.1137/17m1140601","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1140601","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":true,"oa_status":"green","oa_url":"http://pure.iiasa.ac.at/id/eprint/15767/1/10.1137%4017M1140601.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063585796","display_name":"Francesca Maggioni","orcid":"https://orcid.org/0000-0003-3968-1934"},"institutions":[{"id":"https://openalex.org/I11039511","display_name":"University of Bergamo","ror":"https://ror.org/02mbd5571","country_code":"IT","type":"education","lineage":["https://openalex.org/I11039511"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Francesca Maggioni","raw_affiliation_strings":["Department of Management, Economics and Quantitative Methods, University of Bergamo Via dei Caniana 2, 24127 Bergamo, Italy"],"raw_orcid":"https://orcid.org/0000-0003-3968-1934","affiliations":[{"raw_affiliation_string":"Department of Management, Economics and Quantitative Methods, University of Bergamo Via dei Caniana 2, 24127 Bergamo, Italy","institution_ids":["https://openalex.org/I11039511"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002688746","display_name":"Georg Ch. Pflug","orcid":"https://orcid.org/0000-0001-8215-3550"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]},{"id":"https://openalex.org/I1317774081","display_name":"International Institute for Applied Systems Analysis","ror":"https://ror.org/02wfhk785","country_code":"AT","type":"nonprofit","lineage":["https://openalex.org/I1317774081"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Georg Ch. Pflug","raw_affiliation_strings":["Department of Statistics and Operations Research and International Institute for Applied Sys-tems Analysis (IIASA), University of Vienna, Laxenburg, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Operations Research and International Institute for Applied Sys-tems Analysis (IIASA), University of Vienna, Laxenburg, Austria","institution_ids":["https://openalex.org/I1317774081","https://openalex.org/I129774422"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6465,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.84577506,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"29","issue":"1","first_page":"454","last_page":"483"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9997000098228455,"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":0.9997000098228455,"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/T12137","display_name":"Economic theories and models","score":0.9708999991416931,"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"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.955299973487854,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.783428430557251},{"id":"https://openalex.org/keywords/subgradient-method","display_name":"Subgradient method","score":0.7799789905548096},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6178986430168152},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.615748941898346},{"id":"https://openalex.org/keywords/stochastic-programming","display_name":"Stochastic programming","score":0.47775521874427795},{"id":"https://openalex.org/keywords/expected-value","display_name":"Expected value","score":0.45793747901916504},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4549131691455841},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.45386600494384766},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.43632858991622925},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.42239296436309814},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41325074434280396},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36703652143478394},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14362314343452454}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.783428430557251},{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.7799789905548096},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6178986430168152},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.615748941898346},{"id":"https://openalex.org/C137631369","wikidata":"https://www.wikidata.org/wiki/Q7617831","display_name":"Stochastic programming","level":2,"score":0.47775521874427795},{"id":"https://openalex.org/C141042865","wikidata":"https://www.wikidata.org/wiki/Q200125","display_name":"Expected value","level":2,"score":0.45793747901916504},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4549131691455841},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.45386600494384766},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.43632858991622925},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.42239296436309814},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41325074434280396},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36703652143478394},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14362314343452454},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/17m1140601","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1140601","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:pure.iiasa.ac.at:15767","is_oa":true,"landing_page_url":null,"pdf_url":"http://pure.iiasa.ac.at/id/eprint/15767/1/10.1137%4017M1140601.pdf","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"},{"id":"pmh:oai:aisberg.unibg.it:10446/134539","is_oa":true,"landing_page_url":"http://hdl.handle.net/10446/134539","pdf_url":null,"source":{"id":"https://openalex.org/S4377196347","display_name":"Aisberg (University of Bergamo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I11039511","host_organization_name":"University of Bergamo","host_organization_lineage":["https://openalex.org/I11039511"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:pure.iiasa.ac.at:15767","is_oa":true,"landing_page_url":null,"pdf_url":"http://pure.iiasa.ac.at/id/eprint/15767/1/10.1137%4017M1140601.pdf","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2914903271.pdf"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W153653021","https://openalex.org/W1508957056","https://openalex.org/W1821618433","https://openalex.org/W1971454274","https://openalex.org/W1976667494","https://openalex.org/W1977380350","https://openalex.org/W1991890515","https://openalex.org/W2022985650","https://openalex.org/W2023821061","https://openalex.org/W2048305092","https://openalex.org/W2087460341","https://openalex.org/W2097596248","https://openalex.org/W2119407575","https://openalex.org/W2119750259","https://openalex.org/W2126291416","https://openalex.org/W2129636694","https://openalex.org/W2130968988","https://openalex.org/W2142073449","https://openalex.org/W2304662403","https://openalex.org/W2315735804","https://openalex.org/W2329499105","https://openalex.org/W2746381058","https://openalex.org/W3125763446"],"related_works":["https://openalex.org/W4318598368","https://openalex.org/W2012437081","https://openalex.org/W4254717236","https://openalex.org/W2377757044","https://openalex.org/W4221167213","https://openalex.org/W3160952126","https://openalex.org/W2920841750","https://openalex.org/W2320103255","https://openalex.org/W61315285","https://openalex.org/W2105067139"],"abstract_inverted_index":{"In":[0,42],"general,":[1],"multistage":[2,122],"stochastic":[3,36,105],"optimization":[4],"problems":[5,19],"are":[6,20,27,38],"formulated":[7],"on":[8,113],"the":[9,15,34,59,68,72,82,95,103,108],"basis":[10],"of":[11,33,71],"continuous":[12],"distributions":[13],"describing":[14],"uncertainty.":[16],"Such":[17],"\u201cinfinite\u201d":[18],"practically":[21],"impossible":[22],"to":[23],"solve":[24],"as":[25,40],"they":[26],"formulated,":[28],"and":[29,64,111],"finite":[30,54],"tree":[31,55],"approximations":[32,101],"underlying":[35],"processes":[37],"used":[39],"proxies.":[41],"this":[43,86],"paper,":[44],"we":[45],"demonstrate":[46],"how":[47],"one":[48],"can":[49,88],"find":[50],"guaranteed":[51],"bounds,":[52],"i.e.,":[53],"models,":[56],"for":[57,67],"which":[58],"optimal":[60,69],"values":[61],"give":[62],"upper":[63],"lower":[65],"bounds":[66],"value":[70],"original":[73],"infinite":[74],"problem.":[75,125],"Typically,":[76],"there":[77],"is":[78,118],"a":[79,121],"gap":[80,87],"between":[81],"two":[83],"bounds.":[84],"However,":[85],"be":[89],"made":[90],"arbitrarily":[91],"small":[92],"by":[93],"making":[94],"approximating":[96],"trees":[97],"bushier.":[98],"We":[99],"consider":[100],"in":[102,107,120],"first-order":[104],"sense,":[106,110],"convex-order":[109],"based":[112],"subgradient":[114],"approximations.":[115],"Their":[116],"use":[117],"shown":[119],"risk-averse":[123],"production":[124]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2019,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
