{"id":"https://openalex.org/W3128760036","doi":"https://doi.org/10.1007/s40314-021-01431-8","title":"Optimality conditions and duality in terms of convexificators for multiobjective bilevel programming problem with equilibrium constraints","display_name":"Optimality conditions and duality in terms of convexificators for multiobjective bilevel programming problem with equilibrium constraints","publication_year":2021,"publication_date":"2021-02-03","ids":{"openalex":"https://openalex.org/W3128760036","doi":"https://doi.org/10.1007/s40314-021-01431-8","mag":"3128760036"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-021-01431-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-021-01431-8","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","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/A5036127524","display_name":"Tr\u1ea7n V\u0103n S\u1ef1","orcid":"https://orcid.org/0000-0001-9828-554X"},"institutions":[{"id":"https://openalex.org/I4210126982","display_name":"Viet Nam University Of Traditional Medicine","ror":"https://ror.org/02r1dkx80","country_code":"VN","type":"education","lineage":["https://openalex.org/I4210126982"]},{"id":"https://openalex.org/I4400008996","display_name":"Quang Nam University","ror":"https://ror.org/00j4fc191","country_code":null,"type":"education","lineage":["https://openalex.org/I4400008996"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Tran Van Su","raw_affiliation_strings":["Department of Mathematics, Quang Nam University, Tamky, Vietnam"],"raw_orcid":"https://orcid.org/0000-0001-7488-242X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Quang Nam University, Tamky, Vietnam","institution_ids":["https://openalex.org/I4210126982","https://openalex.org/I4400008996"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083589927","display_name":"\u0110inh Di\u1ec7u H\u1eb1ng","orcid":null},"institutions":[{"id":"https://openalex.org/I4210115718","display_name":"Thai Nguyen University","ror":"https://ror.org/02128gy91","country_code":"VN","type":"education","lineage":["https://openalex.org/I4210115718"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Dinh Dieu Hang","raw_affiliation_strings":["Department of Basic Sciences, Thai Nguyen University of Information and Communication Technology, Thai Nguyen, Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Basic Sciences, Thai Nguyen University of Information and Communication Technology, Thai Nguyen, Vietnam","institution_ids":["https://openalex.org/I4210115718"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007261601","display_name":"Nguy\u1ec5n C\u00f4ng \u0110i\u1ec1u","orcid":null},"institutions":[{"id":"https://openalex.org/I4210097659","display_name":"Thang Long University","ror":"https://ror.org/00dd6af44","country_code":"VN","type":"education","lineage":["https://openalex.org/I4210097659"]},{"id":"https://openalex.org/I70349855","display_name":"Vietnam Academy of Science and Technology","ror":"https://ror.org/02wsd5p50","country_code":"VN","type":"government","lineage":["https://openalex.org/I70349855"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Nguyen Cong Dieu","raw_affiliation_strings":["Institute of Information Technology, Vietnam Academy of Science and Technology, Hanoi, Vietnam","Thang Long University, Ha Noi, Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Information Technology, Vietnam Academy of Science and Technology, Hanoi, Vietnam","institution_ids":["https://openalex.org/I70349855"]},{"raw_affiliation_string":"Thang Long University, Ha Noi, Vietnam","institution_ids":["https://openalex.org/I4210097659"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5036127524"],"corresponding_institution_ids":["https://openalex.org/I4210126982","https://openalex.org/I4400008996"],"apc_list":null,"apc_paid":null,"fwci":0.9085,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.77351528,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"40","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9997000098228455,"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":0.9997000098228455,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9771999716758728,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9642000198364258,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/duality","display_name":"Duality (order theory)","score":0.7892376184463501},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.7180502414703369},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6305036544799805},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6245120167732239},{"id":"https://openalex.org/keywords/bilevel-optimization","display_name":"Bilevel optimization","score":0.6056562662124634},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.6003565192222595},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.5778331756591797},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4942300617694855},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.47134917974472046},{"id":"https://openalex.org/keywords/wolfe-duality","display_name":"Wolfe duality","score":0.4635768234729767},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43621155619621277},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.41805270314216614},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.30673426389694214},{"id":"https://openalex.org/keywords/weak-duality","display_name":"Weak duality","score":0.21727785468101501},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12695595622062683},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.07552996277809143}],"concepts":[{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.7892376184463501},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.7180502414703369},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6305036544799805},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6245120167732239},{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.6056562662124634},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6003565192222595},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.5778331756591797},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4942300617694855},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.47134917974472046},{"id":"https://openalex.org/C109456813","wikidata":"https://www.wikidata.org/wiki/Q8029991","display_name":"Wolfe duality","level":5,"score":0.4635768234729767},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43621155619621277},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.41805270314216614},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.30673426389694214},{"id":"https://openalex.org/C80682859","wikidata":"https://www.wikidata.org/wiki/Q7977943","display_name":"Weak duality","level":4,"score":0.21727785468101501},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12695595622062683},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.07552996277809143},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","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},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-021-01431-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-021-01431-8","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W90642534","https://openalex.org/W113278869","https://openalex.org/W1551360398","https://openalex.org/W1553702074","https://openalex.org/W1585268704","https://openalex.org/W1811440824","https://openalex.org/W1966480644","https://openalex.org/W1976076488","https://openalex.org/W1982522297","https://openalex.org/W1983321818","https://openalex.org/W1983644172","https://openalex.org/W1994436307","https://openalex.org/W1997705745","https://openalex.org/W2007152910","https://openalex.org/W2007679787","https://openalex.org/W2030722820","https://openalex.org/W2036389630","https://openalex.org/W2050798859","https://openalex.org/W2052822438","https://openalex.org/W2071707442","https://openalex.org/W2072061819","https://openalex.org/W2091269139","https://openalex.org/W2093404847","https://openalex.org/W2095818975","https://openalex.org/W2124659975","https://openalex.org/W2138849538","https://openalex.org/W2150459262","https://openalex.org/W2210060396","https://openalex.org/W2252823212","https://openalex.org/W2561178549","https://openalex.org/W2587583146","https://openalex.org/W2615258659","https://openalex.org/W2777647696","https://openalex.org/W2781783988","https://openalex.org/W2921168107","https://openalex.org/W2956131074","https://openalex.org/W2996362210","https://openalex.org/W3015956618","https://openalex.org/W3016306595","https://openalex.org/W4231015361","https://openalex.org/W4231147659","https://openalex.org/W4253214256","https://openalex.org/W4292542951"],"related_works":["https://openalex.org/W3213165575","https://openalex.org/W4220928172","https://openalex.org/W4313014939","https://openalex.org/W2029896594","https://openalex.org/W2384039353","https://openalex.org/W2056178476","https://openalex.org/W4283709143","https://openalex.org/W2345066843","https://openalex.org/W2136200239","https://openalex.org/W2030467555"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}