{"id":"https://openalex.org/W2606883349","doi":"https://doi.org/10.1007/s10107-017-1143-6","title":"Distributionally robust optimization with matrix moment constraints: Lagrange duality and cutting plane methods","display_name":"Distributionally robust optimization with matrix moment constraints: Lagrange duality and cutting plane methods","publication_year":2017,"publication_date":"2017-04-12","ids":{"openalex":"https://openalex.org/W2606883349","doi":"https://doi.org/10.1007/s10107-017-1143-6","mag":"2606883349"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-017-1143-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-017-1143-6","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10107-017-1143-6.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs10107-017-1143-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076597279","display_name":"Huifu Xu","orcid":"https://orcid.org/0000-0001-8307-2920"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Huifu Xu","raw_affiliation_strings":["School of Mathematical Sciences, University of Southampton, SO17 1BJ, Southampton, UK"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Southampton, SO17 1BJ, Southampton, UK","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100617985","display_name":"Yongchao Liu","orcid":"https://orcid.org/0000-0001-9955-4414"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongchao Liu","raw_affiliation_strings":["School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034967177","display_name":"Hailin Sun","orcid":"https://orcid.org/0000-0002-1036-6327"},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hailin Sun","raw_affiliation_strings":["School of Economics and Management, Nanjing University of Science and Technology, Nanjing, 210049, China"],"affiliations":[{"raw_affiliation_string":"School of Economics and Management, Nanjing University of Science and Technology, Nanjing, 210049, China","institution_ids":["https://openalex.org/I36399199"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5076597279"],"corresponding_institution_ids":["https://openalex.org/I43439940"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2890},"fwci":6.9886,"has_fulltext":true,"cited_by_count":83,"citation_normalized_percentile":{"value":0.96883175,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"169","issue":"2","first_page":"489","last_page":"529"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9966999888420105,"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"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9879000186920166,"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/mathematics","display_name":"Mathematics","score":0.8498773574829102},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.700948178768158},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.6838182210922241},{"id":"https://openalex.org/keywords/duality-gap","display_name":"Duality gap","score":0.6432446241378784},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6222037672996521},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.5955740809440613},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.5953298807144165},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.4823255240917206},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47696006298065186},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.4742409586906433},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.42439451813697815},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.37363186478614807},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24687081575393677},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.16166231036186218}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8498773574829102},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.700948178768158},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.6838182210922241},{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.6432446241378784},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6222037672996521},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.5955740809440613},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.5953298807144165},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.4823255240917206},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47696006298065186},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4742409586906433},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.42439451813697815},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.37363186478614807},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24687081575393677},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16166231036186218},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10107-017-1143-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-017-1143-6","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10107-017-1143-6.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:eprints.soton.ac.uk:407211","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1007/s10107-017-1143-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-017-1143-6","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10107-017-1143-6.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1294958814","display_name":null,"funder_award_id":"11401308","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2030376154","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3910829908","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7261742914","display_name":null,"funder_award_id":"BK20140768","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G8522932942","display_name":"Distributionally Robust Optimisation With Matrix Moment Constraints: A Semi-Infinite and Semi-Definite Programming Approach","funder_award_id":"EP/M003191/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8616016700","display_name":null,"funder_award_id":"EP/M003191/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8902815113","display_name":null,"funder_award_id":"201407","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320277","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321605","display_name":"Government of Jiangsu Province","ror":"https://ror.org/004svx814"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2606883349.pdf","grobid_xml":"https://content.openalex.org/works/W2606883349.grobid-xml"},"referenced_works_count":63,"referenced_works":["https://openalex.org/W11808602","https://openalex.org/W141136562","https://openalex.org/W227597898","https://openalex.org/W622935592","https://openalex.org/W1490324987","https://openalex.org/W1518992076","https://openalex.org/W1541527977","https://openalex.org/W1551360398","https://openalex.org/W1570220941","https://openalex.org/W1601741115","https://openalex.org/W1647779468","https://openalex.org/W1855391364","https://openalex.org/W1964730816","https://openalex.org/W1967331745","https://openalex.org/W1968355947","https://openalex.org/W1971867489","https://openalex.org/W1983609582","https://openalex.org/W1993377828","https://openalex.org/W1993599556","https://openalex.org/W1999560794","https://openalex.org/W1999913571","https://openalex.org/W2007421997","https://openalex.org/W2021097403","https://openalex.org/W2035238076","https://openalex.org/W2041219907","https://openalex.org/W2043157166","https://openalex.org/W2052889677","https://openalex.org/W2061293389","https://openalex.org/W2069099760","https://openalex.org/W2069808690","https://openalex.org/W2074499214","https://openalex.org/W2080474145","https://openalex.org/W2082477992","https://openalex.org/W2087737604","https://openalex.org/W2092660864","https://openalex.org/W2092866161","https://openalex.org/W2109518176","https://openalex.org/W2117781171","https://openalex.org/W2119303899","https://openalex.org/W2125417745","https://openalex.org/W2128244396","https://openalex.org/W2131939929","https://openalex.org/W2140214428","https://openalex.org/W2155153696","https://openalex.org/W2156168813","https://openalex.org/W2164261482","https://openalex.org/W2166292404","https://openalex.org/W2254463431","https://openalex.org/W2510698054","https://openalex.org/W2558813012","https://openalex.org/W2562747313","https://openalex.org/W2605458048","https://openalex.org/W2608217951","https://openalex.org/W2618093839","https://openalex.org/W2798202585","https://openalex.org/W2802739963","https://openalex.org/W2964297002","https://openalex.org/W3048259557","https://openalex.org/W3098173350","https://openalex.org/W4247165901","https://openalex.org/W4249513058","https://openalex.org/W4251616545","https://openalex.org/W4298050965"],"related_works":["https://openalex.org/W4220928172","https://openalex.org/W2725387418","https://openalex.org/W2201555914","https://openalex.org/W2593555778","https://openalex.org/W2614523486","https://openalex.org/W2080941243","https://openalex.org/W2136200239","https://openalex.org/W2056178476","https://openalex.org/W3213165575","https://openalex.org/W1687657632"],"abstract_inverted_index":{"A":[0],"key":[1],"step":[2],"in":[3,174],"solving":[4,89],"minimax":[5,160],"distributionally":[6],"robust":[7],"optimization":[8],"(DRO)":[9],"problems":[10],"is":[11,45,168],"to":[12],"reformulate":[13],"the":[14,42,58,73,78,90,95,99,103,107,110,115,127,131,134,151,156,159,171,177,191],"inner":[15,79],"maximization":[16,80],"w.r.t.":[17],"probability":[18],"measure":[19],"as":[20],"a":[21,139],"semiinfinite":[22],"programming":[23],"problem":[24],"through":[25,47,102],"Lagrange":[26,119],"dual.":[27],"Slater":[28,59],"type":[29,60],"conditions":[30,61,65],"have":[31],"been":[32],"widely":[33],"used":[34],"for":[35,56,88,94,126,150,158,170,190],"strong":[36,113],"duality":[37,120],"(zero":[38],"dual":[39],"gap)":[40],"when":[41],"ambiguity":[43,104,164],"set":[44,105],"defined":[46],"moments.":[48],"In":[49,109],"this":[50],"paper,":[51],"we":[52,83],"investigate":[53],"effective":[54],"ways":[55],"verifying":[57],"and":[62,98,155,182],"introduce":[63],"other":[64,100,157],"which":[66],"are":[67,146,188],"based":[68],"on":[69],"lower":[70,140],"semicontinuity":[71],"of":[72,77,106,112,130,176],"optimal":[74,128,178,180],"value":[75,129],"function":[76],"problem.":[81],"Moreover,":[82],"propose":[84],"two":[85],"discretization":[86,116,136],"schemes":[87,145,173],"DRO":[91,97,132,154,161],"with":[92,162],"one":[93,149],"dualized":[96,153],"directly":[101],"DRO.":[108],"absence":[111],"duality,":[114],"scheme":[117],"via":[118],"may":[121],"provide":[122],"an":[123],"upper":[124],"bound":[125],"whereas":[133],"direct":[135],"approach":[137],"provides":[138],"bound.":[141],"Two":[142],"cutting":[143],"plane":[144],"consequently":[147],"proposed:":[148],"discretized":[152,163],"set.":[165],"Convergence":[166],"analysis":[167],"presented":[169],"approximation":[172],"terms":[175],"value,":[179],"solutions":[181],"stationary":[183],"points.":[184],"Comparative":[185],"numerical":[186],"results":[187],"reported":[189],"resulting":[192],"algorithms.":[193]},"counts_by_year":[{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}