{"id":"https://openalex.org/W2626014635","doi":"https://doi.org/10.1137/16m1067925","title":"A Unified Approach to Robust Farkas-Type Results with Applications to Robust Optimization Problems","display_name":"A Unified Approach to Robust Farkas-Type Results with Applications to Robust Optimization Problems","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2626014635","doi":"https://doi.org/10.1137/16m1067925","mag":"2626014635"},"language":"en","primary_location":{"id":"doi:10.1137/16m1067925","doi":"https://doi.org/10.1137/16m1067925","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1067925","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,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-1","norway-2","poland-140","russia-white-list-1"],"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"},"parent_works":[],"lineage":["https://openalex.org/W2626014635"],"child_works_count":0,"type":"article","is_traditional":true,"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":null,"display_name":"N. Dinh","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"N. Dinh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058839960","display_name":"T. H. Mo","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"T. H. Mo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040291813","display_name":"Guy Vallet","orcid":"https://orcid.org/0000-0001-7543-9796","observed_orcids":["https://orcid.org/0000-0001-7543-9796"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G. Vallet","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109636926","display_name":"Michel Volle","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4405266840","display_name":"Laboratoire de Math\u00e9matiques d'Avignon","ror":"https://ror.org/000d7xf38","country_code":"FR","type":"education","lineage":["https://openalex.org/I198415970","https://openalex.org/I4405266840"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"M. Volle","raw_affiliation_strings":["EA2151 Laboratoire de Math\u00e9matiques d'Avignon"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"EA2151 Laboratoire de Math\u00e9matiques d'Avignon","institution_ids":["https://openalex.org/I4405266840"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.9492,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.84792755,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"27","issue":"2","first_page":"1075","last_page":"1101"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9932000041007996,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9932000041007996,"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"}},{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.002199999988079071,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.0017000000225380063,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/robust-optimization","display_name":"robust optimization","score":0.8309999704360962},{"id":"https://openalex.org/keywords/dc-optimization","display_name":"DC optimization","score":0.5419999957084656},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"convex optimization","score":0.6700000166893005},{"id":"https://openalex.org/keywords/uncertainty-sets","display_name":"uncertainty sets","score":0.4259999990463257}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8511248826980591},{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.5294767618179321},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.5152595043182373},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.48654213547706604},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4729188084602356},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47102198004722595},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.43943700194358826},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36204642057418823},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33891528844833374},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0947386622428894},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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:10.1137/16m1067925","doi":"https://doi.org/10.1137/16m1067925","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1067925","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,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-1","norway-2","poland-140","russia-white-list-1"],"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:HAL:hal-01759889v1","doi":null,"is_oa":false,"landing_page_url":"https://hal.science/hal-01759889","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Optimization, 2017, 27 (2), pp.1075--1101. &#x27E8;10.1137/16M1067925&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-03438214v1","doi":null,"is_oa":false,"landing_page_url":"https://univ-avignon.hal.science/hal-03438214","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Optimization, 2017, 27 (2), pp.1075-1101. &#x27E8;10.1137/16M1067925&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W85096072","https://openalex.org/W1504946885","https://openalex.org/W1982099023","https://openalex.org/W1999737152","https://openalex.org/W2000285254","https://openalex.org/W2010724422","https://openalex.org/W2024038716","https://openalex.org/W2049801480","https://openalex.org/W2063449703","https://openalex.org/W2099118332","https://openalex.org/W2103632601","https://openalex.org/W2114397143","https://openalex.org/W2114605231","https://openalex.org/W2134919172","https://openalex.org/W2140496876","https://openalex.org/W2152533835","https://openalex.org/W2333887093","https://openalex.org/W2579396829","https://openalex.org/W3021970279","https://openalex.org/W4249125060","https://openalex.org/W4251616545"],"related_works":["https://openalex.org/W2127855168","https://openalex.org/W2887469404","https://openalex.org/W7214469267","https://openalex.org/W4286461814","https://openalex.org/W2322044356","https://openalex.org/W2791753995","https://openalex.org/W3010604882","https://openalex.org/W4298086125","https://openalex.org/W1973524432","https://openalex.org/W2333887093"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"consider":[4],"the":[5,8],"inequality":[6,64],"of":[7,61,67,85,135,154],"form":[9],"$":[10],"\\sup_{u":[11],"\\in":[12,45],"\\mathcal{U}}":[13],"F_u(\\cdot,":[14],"0_Y)":[15],"\\geq":[16],"h,$":[17],"where":[18],"$X,":[19],"Y$":[20],"are":[21,72,130,157],"locally":[22],"convex":[23,58,110,140],"Hausdorff":[24],"topological":[25],"vector":[26],"spaces,":[27,122],"$\\mathcal{U}":[28],"\\not=":[29],"\\emptyset$":[30],"is":[31,53],"an":[32,63],"uncertainty":[33],"set,":[34],"$F_u":[35],":":[36,49],"X":[37,50],"\\times":[38],"Y":[39],"\\rightarrow":[40,51],"\\overline{\\mathbb{R}}$":[41,52],"for":[42,94,102,109,115,151],"each":[43],"$u":[44],"\\mathcal{U}$,":[46],"and":[47,74,123,138,143,147],"$h":[48],"a":[54],"lower":[55],"semicontinuous":[56],"proper":[57],"function.":[59],"Characterizations":[60],"such":[62,89],"in":[65,119],"terms":[66],"robust":[68,78,86,91,99,106,112,124,136,139,155],"abstract":[69],"perturbational":[70],"duality":[71,146,150],"established":[73],"applied":[75,132],"to":[76,82,133],"diverse":[77],"composite":[79],"functional":[80],"inequalities":[81],"obtain":[83],"variants":[84],"Farkas-type":[87],"results,":[88],"as":[90],"Farkas":[92,100,107,113,126],"lemmas":[93,101,108,114],"general":[95,116],"nonconvex":[96],"conical":[97],"systems,":[98,104,111],"convex-DC":[103],"robust/stable":[105],"linear":[117],"systems":[118],"infinite":[120],"dimensional":[121],"semi-infinite":[125],"lemmas.":[127],"The":[128],"results":[129],"then":[131],"classes":[134,153],"DC":[137],"optimization":[141],"problems,":[142],"strong":[144],"Fenchel":[145],"stable-strong/strong":[148],"Lagrange":[149],"these":[152],"problems":[156],"obtained.":[158]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2017-06-23T00:00:00"}
