{"id":"https://openalex.org/W4398771499","doi":"https://doi.org/10.1051/ro/2024118","title":"Higher-order optimality conditions with separated derivatives and sensitivity analysis for set-valued optimization","display_name":"Higher-order optimality conditions with separated derivatives and sensitivity analysis for set-valued optimization","publication_year":2024,"publication_date":"2024-05-24","ids":{"openalex":"https://openalex.org/W4398771499","doi":"https://doi.org/10.1051/ro/2024118"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2024118","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ro/2024118","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/04/ro230703.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/04/ro230703.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5106544229","display_name":"Tian Tang","orcid":"https://orcid.org/0009-0009-8387-3037"},"institutions":[{"id":"https://openalex.org/I21642278","display_name":"Ningxia University","ror":"https://ror.org/04j7b2v61","country_code":"CN","type":"education","lineage":["https://openalex.org/I21642278"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tian Tang","raw_affiliation_strings":["School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, P.R. China","institution_ids":["https://openalex.org/I21642278"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076538595","display_name":"Guolin Yu","orcid":"https://orcid.org/0000-0003-4729-7748"},"institutions":[{"id":"https://openalex.org/I3019309368","display_name":"North Minzu University","ror":"https://ror.org/05xjevr11","country_code":"CN","type":"education","lineage":["https://openalex.org/I3019309368"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guolin Yu","raw_affiliation_strings":["School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, P.R. China","institution_ids":["https://openalex.org/I3019309368"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2882,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.5539681,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"58","issue":"4","first_page":"3049","last_page":"3067"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9711999893188477,"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":0.9711999893188477,"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/sensitivity","display_name":"Sensitivity (control systems)","score":0.7900020480155945},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6068743467330933},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5955511331558228},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5223225951194763},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.46109142899513245},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3204473853111267},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.09303811192512512},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.09287694096565247}],"concepts":[{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.7900020480155945},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6068743467330933},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5955511331558228},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5223225951194763},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46109142899513245},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3204473853111267},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.09303811192512512},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.09287694096565247},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","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},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1051/ro/2024118","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ro/2024118","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/04/ro230703.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1051/ro/2024118","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ro/2024118","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/04/ro230703.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1819250203","display_name":null,"funder_award_id":"12361062","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2881086398","display_name":null,"funder_award_id":"62366001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8217285324","display_name":null,"funder_award_id":"2023AAC02053","funder_id":"https://openalex.org/F4320322877","funder_display_name":"Natural Science Foundation of Ningxia Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322877","display_name":"Natural Science Foundation of Ningxia Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4398771499.pdf","grobid_xml":"https://content.openalex.org/works/W4398771499.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W187778025","https://openalex.org/W1967764519","https://openalex.org/W1972675155","https://openalex.org/W1977142340","https://openalex.org/W2002894912","https://openalex.org/W2008022968","https://openalex.org/W2020885309","https://openalex.org/W2027200819","https://openalex.org/W2030967943","https://openalex.org/W2057088466","https://openalex.org/W2101738640","https://openalex.org/W2313919514","https://openalex.org/W2339349320","https://openalex.org/W2343204853","https://openalex.org/W2478963760","https://openalex.org/W2523142878","https://openalex.org/W2620691315","https://openalex.org/W3027366238","https://openalex.org/W3030147163","https://openalex.org/W3049735886","https://openalex.org/W3215884205","https://openalex.org/W4223433874","https://openalex.org/W4249125060","https://openalex.org/W4313677174","https://openalex.org/W4391776005"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"In":[0],"this":[1,75],"paper,":[2],"we":[3,21],"establish":[4],"optimality":[5,24],"conditions":[6,25],"and":[7,42],"sensitivity":[8,67],"analysis":[9,68],"of":[10,16,40,55,74],"set-valued":[11,31,57],"optimization":[12,32,58],"problems":[13],"in":[14],"terms":[15],"higher-order":[17,66],"radial":[18],"derivatives.":[19],"First,":[20],"obtain":[22],"the":[23,38],"with":[26],"separated":[27,35],"derivatives":[28,36,39],"for":[29,51],"a":[30,52],"problem,":[33],"here":[34],"means":[37],"objective":[41],"constraint":[43],"functions":[44],"are":[45,60,69,77],"different.":[46],"Then,":[47],"some":[48,80],"duality":[49],"theorems":[50],"mixed":[53],"type":[54],"primal-dual":[56],"problem":[59],"gained.":[61],"Finally,":[62],"several":[63],"results":[64,73],"concerning":[65],"presented.":[70],"The":[71],"main":[72],"paper":[76],"illustrated":[78],"by":[79],"concrete":[81],"examples.":[82]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-07T06:14:10.401900","created_date":"2025-10-10T00:00:00"}