{"id":"https://openalex.org/W3179558415","doi":"https://doi.org/10.1137/19m1290115","title":"Efficient Algorithms for Distributionally Robust Stochastic Optimization with Discrete Scenario Support","display_name":"Efficient Algorithms for Distributionally Robust Stochastic Optimization with Discrete Scenario Support","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3179558415","doi":"https://doi.org/10.1137/19m1290115","mag":"3179558415"},"language":"en","primary_location":{"id":"doi:10.1137/19m1290115","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1290115","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/A5100443023","display_name":"Zhe Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhe Zhang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027399293","display_name":"Shabbir Ahmed","orcid":"https://orcid.org/0000-0001-7049-7305"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shabbir Ahmed","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5042544900","display_name":"Guanghui Lan","orcid":"https://orcid.org/0000-0002-2103-087X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guanghui Lan","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100443023"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2529,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.80610075,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"31","issue":"3","first_page":"1690","last_page":"1721"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9998999834060669,"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":0.9998999834060669,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.982200026512146,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6519019603729248},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6300567388534546},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4868883192539215},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4827386736869812},{"id":"https://openalex.org/keywords/ambiguity","display_name":"Ambiguity","score":0.4783701002597809},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.458736777305603},{"id":"https://openalex.org/keywords/stochastic-programming","display_name":"Stochastic programming","score":0.4528312683105469},{"id":"https://openalex.org/keywords/robust-optimization","display_name":"Robust optimization","score":0.4433208107948303},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4368681311607361},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.424453467130661},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30972856283187866}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6519019603729248},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6300567388534546},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4868883192539215},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4827386736869812},{"id":"https://openalex.org/C2780522230","wikidata":"https://www.wikidata.org/wiki/Q1140419","display_name":"Ambiguity","level":2,"score":0.4783701002597809},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.458736777305603},{"id":"https://openalex.org/C137631369","wikidata":"https://www.wikidata.org/wiki/Q7617831","display_name":"Stochastic programming","level":2,"score":0.4528312683105469},{"id":"https://openalex.org/C193254401","wikidata":"https://www.wikidata.org/wiki/Q2160088","display_name":"Robust optimization","level":2,"score":0.4433208107948303},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4368681311607361},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.424453467130661},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30972856283187866},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1290115","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1290115","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":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7099999785423279}],"awards":[{"id":"https://openalex.org/G2278043753","display_name":null,"funder_award_id":"W911NF-18-1-0223","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1542523037","https://openalex.org/W1971867489","https://openalex.org/W2000257769","https://openalex.org/W2006118023","https://openalex.org/W2033957915","https://openalex.org/W2038407338","https://openalex.org/W2053434217","https://openalex.org/W2082569121","https://openalex.org/W2167732364","https://openalex.org/W2241435520","https://openalex.org/W2766425587","https://openalex.org/W2793108066","https://openalex.org/W2963450292","https://openalex.org/W2964268944","https://openalex.org/W2965299328","https://openalex.org/W2969945254","https://openalex.org/W3097661180"],"related_works":["https://openalex.org/W4293570283","https://openalex.org/W1996228459","https://openalex.org/W2745418069","https://openalex.org/W2978562669","https://openalex.org/W2127331687","https://openalex.org/W3204714198","https://openalex.org/W308707143","https://openalex.org/W2154626019","https://openalex.org/W2062144119","https://openalex.org/W2949527903"],"abstract_inverted_index":{"Recently,":[0],"there":[1],"has":[2,40],"been":[3,41],"a":[4,13,25,91,148],"growing":[5],"interest":[6],"in":[7,118,127],"distributionally":[8,26],"robust":[9,27],"optimization":[10,30],"(DRO)":[11],"as":[12,90],"principled":[14],"approach":[15],"to":[16,43,154,179],"data-driven":[17],"decision":[18],"making.":[19],"In":[20],"this":[21],"paper,":[22],"we":[23,146],"consider":[24],"two-stage":[28],"stochastic":[29],"problem":[31,89,96],"with":[32,51,140],"discrete":[33],"scenario":[34,53],"support.":[35],"While":[36],"much":[37],"research":[38],"effort":[39],"devoted":[42],"tractable":[44],"reformulations":[45],"for":[46,132],"DRO":[47,88,138],"problems,":[48],"especially":[49],"those":[50],"continuous":[52],"support,":[54],"few":[55],"efficient":[56],"numerical":[57,175],"algorithms":[58,100,123,153],"are":[59,177],"developed,":[60],"and":[61,97],"most":[62],"of":[63,77,121,137,151,159,167,184],"them":[64],"can":[65,102,124],"neither":[66],"handle":[67],"the":[68,74,83,87,141,156,160,165,181,185],"nonsmooth":[69],"second-stage":[70],"cost":[71],"function":[72],"nor":[73],"large":[75],"number":[76],"scenarios":[78],"$K$":[79],"effectively.":[80],"We":[81],"fill":[82],"gap":[84],"by":[85],"reformulating":[86],"trilinear":[92],"min-max-max":[93],"saddle":[94],"point":[95],"developing":[98],"novel":[99],"that":[101],"achieve":[103],"an":[104,134,168],"$\\mathcal{O}(1/\\epsilon)$":[105],"iteration":[106,120],"complexity":[107],"which":[108],"only":[109],"mildly":[110],"depends":[111],"on":[112],"$K$.":[113],"The":[114],"major":[115],"computations":[116],"involved":[117],"each":[119],"these":[122],"be":[125],"conducted":[126,178],"parallel":[128],"if":[129],"necessary.":[130],"Besides,":[131],"solving":[133],"important":[135],"class":[136],"problems":[139],"Kantorovich":[142],"ball":[143],"ambiguity":[144],"set,":[145],"propose":[147],"slight":[149],"modification":[150],"our":[152],"avoid":[155],"expensive":[157],"computation":[158],"probability":[161],"vector":[162],"projection":[163],"at":[164],"price":[166],"$\\mathcal{O}(\\sqrt{K})$":[169],"times":[170],"more":[171],"iterations.":[172],"Finally,":[173],"preliminary":[174],"experiments":[176],"demonstrate":[180],"empirical":[182],"advantages":[183],"proposed":[186],"algorithms.":[187]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3}],"updated_date":"2026-03-31T07:56:22.981413","created_date":"2025-10-10T00:00:00"}
