{"id":"https://openalex.org/W4400540323","doi":"https://doi.org/10.1287/moor.2022.0122","title":"Rockafellian Relaxation and Stochastic Optimization Under Perturbations","display_name":"Rockafellian Relaxation and Stochastic Optimization Under Perturbations","publication_year":2024,"publication_date":"2024-07-11","ids":{"openalex":"https://openalex.org/W4400540323","doi":"https://doi.org/10.1287/moor.2022.0122"},"language":"en","primary_location":{"id":"doi:10.1287/moor.2022.0122","is_oa":false,"landing_page_url":"https://doi.org/10.1287/moor.2022.0122","pdf_url":null,"source":{"id":"https://openalex.org/S55826652","display_name":"Mathematics of Operations Research","issn_l":"0364-765X","issn":["0364-765X","1526-5471"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Operations Research","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/A5043616688","display_name":"Johannes \u00d8. R\u00f8yset","orcid":"https://orcid.org/0009-0003-3554-7305"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Johannes O. Royset","raw_affiliation_strings":["Industrial and Systems Engineering, University of Southern California, Los Angeles, California 90007","Industrial and Systems Engineering, University of Southern California, Los Angeles, California 90007;"],"raw_orcid":"https://orcid.org/0009-0003-3554-7305","affiliations":[{"raw_affiliation_string":"Industrial and Systems Engineering, University of Southern California, Los Angeles, California 90007","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"Industrial and Systems Engineering, University of Southern California, Los Angeles, California 90007;","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065340334","display_name":"Louis Chen","orcid":"https://orcid.org/0000-0001-5311-7294"},"institutions":[{"id":"https://openalex.org/I35364215","display_name":"Naval Postgraduate School","ror":"https://ror.org/033yfkj90","country_code":"US","type":"education","lineage":["https://openalex.org/I1330347796","https://openalex.org/I3130687028","https://openalex.org/I35364215"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Louis L. Chen","raw_affiliation_strings":["Operations Research, Naval Postgraduate School, Monterey, California 93943"],"raw_orcid":"https://orcid.org/0000-0001-5311-7294","affiliations":[{"raw_affiliation_string":"Operations Research, Naval Postgraduate School, Monterey, California 93943","institution_ids":["https://openalex.org/I35364215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081959838","display_name":"Eric Eckstrand","orcid":"https://orcid.org/0009-0006-2932-8458"},"institutions":[{"id":"https://openalex.org/I35364215","display_name":"Naval Postgraduate School","ror":"https://ror.org/033yfkj90","country_code":"US","type":"education","lineage":["https://openalex.org/I1330347796","https://openalex.org/I3130687028","https://openalex.org/I35364215"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Eric Eckstrand","raw_affiliation_strings":["Operations Research, Naval Postgraduate School, Monterey, California 93943"],"raw_orcid":"https://orcid.org/0009-0006-2932-8458","affiliations":[{"raw_affiliation_string":"Operations Research, Naval Postgraduate School, Monterey, California 93943","institution_ids":["https://openalex.org/I35364215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1646,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.87918426,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"50","issue":"3","first_page":"1585","last_page":"1610"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9941999912261963,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9868000149726868,"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":0.7614894509315491},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5829954147338867},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.5294700860977173},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5058343410491943},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3979644775390625},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35842522978782654}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7614894509315491},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5829954147338867},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.5294700860977173},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5058343410491943},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3979644775390625},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35842522978782654},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1287/moor.2022.0122","is_oa":false,"landing_page_url":"https://doi.org/10.1287/moor.2022.0122","pdf_url":null,"source":{"id":"https://openalex.org/S55826652","display_name":"Mathematics of Operations Research","issn_l":"0364-765X","issn":["0364-765X","1526-5471"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Operations Research","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7200000286102295,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W1484551447","https://openalex.org/W1542523037","https://openalex.org/W1839996114","https://openalex.org/W1968787489","https://openalex.org/W1980131437","https://openalex.org/W1980271923","https://openalex.org/W1982200089","https://openalex.org/W1990467625","https://openalex.org/W1993159399","https://openalex.org/W2006093909","https://openalex.org/W2008832947","https://openalex.org/W2010724422","https://openalex.org/W2011529109","https://openalex.org/W2021067057","https://openalex.org/W2027982384","https://openalex.org/W2048225885","https://openalex.org/W2076694117","https://openalex.org/W2084590216","https://openalex.org/W2114397143","https://openalex.org/W2114605231","https://openalex.org/W2115001337","https://openalex.org/W2117156423","https://openalex.org/W2125417745","https://openalex.org/W2131116400","https://openalex.org/W2136953603","https://openalex.org/W2147837458","https://openalex.org/W2165530668","https://openalex.org/W2397080394","https://openalex.org/W2401014899","https://openalex.org/W2844677341","https://openalex.org/W2954224188","https://openalex.org/W2963450292","https://openalex.org/W2981528476","https://openalex.org/W2997549357","https://openalex.org/W3121059311","https://openalex.org/W3121149831","https://openalex.org/W3162462085","https://openalex.org/W3197941240","https://openalex.org/W4214631981","https://openalex.org/W4229650096","https://openalex.org/W4229984434","https://openalex.org/W4245681537","https://openalex.org/W4246616525","https://openalex.org/W4249513058","https://openalex.org/W4249667877","https://openalex.org/W4251616545","https://openalex.org/W4293820388"],"related_works":["https://openalex.org/W2084105443","https://openalex.org/W2091618907","https://openalex.org/W226927276","https://openalex.org/W2042625933","https://openalex.org/W1993968197","https://openalex.org/W2107527645","https://openalex.org/W2033676864","https://openalex.org/W1978788088","https://openalex.org/W2412311587","https://openalex.org/W4388209346"],"abstract_inverted_index":{"In":[0],"practice,":[1],"optimization":[2,46,83,109],"models":[3],"are":[4,99],"often":[5],"prone":[6],"to":[7,69,102,115,157],"unavoidable":[8],"inaccuracies":[9],"because":[10],"of":[11,62,80,112,118,127,134,145,149,166,174,182,204],"dubious":[12],"assumptions":[13,167],"and":[14,24,27,95,129,154,171,185,222],"corrupted":[15],"data.":[16],"Traditionally,":[17],"this":[18],"placed":[19],"special":[20],"emphasis":[21],"on":[22,30,41,123],"risk-based":[23],"robust":[25],"formulations,":[26],"their":[28],"focus":[29],"\u201cconservative\u201d":[31],"decisions.":[32],"We":[33,98,141],"develop,":[34],"in":[35,44,107,138,179,220],"contrast,":[36],"an":[37],"\u201coptimistic\u201d":[38],"framework":[39,66,121],"based":[40],"Rockafellian":[42,227],"relaxations":[43],"which":[45],"is":[47,164],"conducted":[48],"not":[49],"only":[50],"over":[51],"the":[52,78,104,124,143,180,192,200,211],"original":[53],"decision":[54],"space":[55],"but":[56],"also":[57,100],"jointly":[58],"with":[59,73,132,188],"a":[60],"choice":[61],"model":[63],"perturbation.":[64],"The":[65,120,161],"enables":[67],"us":[68],"address":[70],"challenging":[71],"problems":[72],"ambiguous":[74],"probability":[75,88],"distributions":[76,113],"from":[77,226],"areas":[79],"two-stage":[81],"stochastic":[82,108],"without":[84],"relatively":[85],"complete":[86],"recourse,":[87],"functions":[89],"lacking":[90],"continuity":[91,173],"properties,":[92],"expectation":[93],"constraints,":[94],"outlier":[96],"analysis.":[97],"able":[101],"circumvent":[103],"fundamental":[105],"difficulty":[106],"that":[110],"convergence":[111,117,150],"fails":[114],"guarantee":[116],"expectations.":[119],"centers":[122],"novel":[125],"concepts":[126],"exact":[128],"limit-exact":[130],"Rockafellians,":[131],"interpretations":[133],"\u201cnegative\u201d":[135],"regularization":[136],"emerging":[137],"certain":[139],"settings.":[140],"illustrate":[142,191],"role":[144],"Phi-divergence,":[146],"examine":[147],"rates":[148],"under":[151,210,216],"changing":[152],"distributions,":[153],"explore":[155],"extensions":[156],"first-order":[158],"optimality":[159],"conditions.":[160],"main":[162],"development":[163],"free":[165],"about":[168],"convexity,":[169],"smoothness,":[170],"even":[172],"objective":[175],"functions.":[176],"Numerical":[177],"results":[178],"setting":[181],"computer":[183],"vision":[184],"text":[186],"analytics":[187],"label":[189],"noise":[190],"framework.":[193],"Funding:":[194],"This":[195],"work":[196],"was":[197],"supported":[198],"by":[199],"Air":[201],"Force":[202],"Office":[203],"Scientific":[205],"Research":[206],"(Mathematical":[207],"Optimization":[208],"Program)":[209],"grant:":[212],"\u201cOptimal":[213],"Decision":[214],"Making":[215],"Tight":[217],"Performance":[218],"Requirements":[219],"Adversarial":[221],"Uncertain":[223],"Environments:":[224],"Insight":[225],"Functions.\u201d":[228]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
