{"id":"https://openalex.org/W7169578008","doi":"https://doi.org/10.1007/s10957-026-03061-8","title":"Some Characteristics of the Solution for Extended Vertical Tensor Complementarity Problem","display_name":"Some Characteristics of the Solution for Extended Vertical Tensor Complementarity Problem","publication_year":2026,"publication_date":"2026-07-17","ids":{"openalex":"https://openalex.org/W7169578008","doi":"https://doi.org/10.1007/s10957-026-03061-8"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-026-03061-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-026-03061-8","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","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/A5113367146","display_name":"Zu-Feng Fu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210110718","display_name":"Nanyang Normal University","ror":"https://ror.org/01f7yer47","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210110718"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zu-Feng Fu","raw_affiliation_strings":["Henan Collaborative Innovation Center of Intelligent Explosion-proof Equipment, Nanyang Normal University, Nanyang, Henan, 473061, P.R. China","School of Artificial Intelligence and Software Engineering, Nanyang Normal University, Nanyang, Henan, 473061, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Henan Collaborative Innovation Center of Intelligent Explosion-proof Equipment, Nanyang Normal University, Nanyang, Henan, 473061, P.R. China","institution_ids":["https://openalex.org/I4210110718"]},{"raw_affiliation_string":"School of Artificial Intelligence and Software Engineering, Nanyang Normal University, Nanyang, Henan, 473061, P.R. China","institution_ids":["https://openalex.org/I4210110718"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5115695209","display_name":"Haiying Wang","orcid":"https://orcid.org/0009-0009-7643-1804"},"institutions":[{"id":"https://openalex.org/I4210110718","display_name":"Nanyang Normal University","ror":"https://ror.org/01f7yer47","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210110718"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hai-Ying Wang","raw_affiliation_strings":["Henan Collaborative Innovation Center of Intelligent Explosion-proof Equipment, Nanyang Normal University, Nanyang, Henan, 473061, P.R. China","School of Artificial Intelligence and Software Engineering, Nanyang Normal University, Nanyang, Henan, 473061, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Henan Collaborative Innovation Center of Intelligent Explosion-proof Equipment, Nanyang Normal University, Nanyang, Henan, 473061, P.R. China","institution_ids":["https://openalex.org/I4210110718"]},{"raw_affiliation_string":"School of Artificial Intelligence and Software Engineering, Nanyang Normal University, Nanyang, Henan, 473061, P.R. China","institution_ids":["https://openalex.org/I4210110718"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061480695","display_name":"Shi-Liang Wu","orcid":"https://orcid.org/0000-0002-7798-3557"},"institutions":[{"id":"https://openalex.org/I120825670","display_name":"Yunnan Normal University","ror":"https://ror.org/00sc9n023","country_code":"CN","type":"education","lineage":["https://openalex.org/I120825670"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shi-Liang Wu","raw_affiliation_strings":["School of Mathematics, Yunnan Normal University, Kunming, Yunnan, 650500, P.R. China","Yunnan Key Laboratory of Modern Analytical Mathematics and Applications, Yunnan Normal University, Kunming, Yunnan, 650500, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Yunnan Normal University, Kunming, Yunnan, 650500, P.R. China","institution_ids":["https://openalex.org/I120825670"]},{"raw_affiliation_string":"Yunnan Key Laboratory of Modern Analytical Mathematics and Applications, Yunnan Normal University, Kunming, Yunnan, 650500, P.R. China","institution_ids":["https://openalex.org/I120825670"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061480695"],"corresponding_institution_ids":["https://openalex.org/I120825670"],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.74774775,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"210","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9628000259399414,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9628000259399414,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.020600000396370888,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.002899999963119626,"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/complementarity-theory","display_name":"Complementarity theory","score":0.7511000037193298},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6866000294685364},{"id":"https://openalex.org/keywords/complementarity","display_name":"Complementarity (molecular biology)","score":0.673799991607666},{"id":"https://openalex.org/keywords/mixed-complementarity-problem","display_name":"Mixed complementarity problem","score":0.6694999933242798},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.4921000003814697},{"id":"https://openalex.org/keywords/solution-set","display_name":"Solution set","score":0.4417000114917755},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.37040001153945923}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7813000082969666},{"id":"https://openalex.org/C85404239","wikidata":"https://www.wikidata.org/wiki/Q5156417","display_name":"Complementarity theory","level":3,"score":0.7511000037193298},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6866000294685364},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.673799991607666},{"id":"https://openalex.org/C77196050","wikidata":"https://www.wikidata.org/wiki/Q6883962","display_name":"Mixed complementarity problem","level":3,"score":0.6694999933242798},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.4921000003814697},{"id":"https://openalex.org/C60033838","wikidata":"https://www.wikidata.org/wiki/Q1751685","display_name":"Solution set","level":3,"score":0.4417000114917755},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38600000739097595},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.37040001153945923},{"id":"https://openalex.org/C2778646529","wikidata":"https://www.wikidata.org/wiki/Q16948724","display_name":"Nonlinear complementarity problem","level":4,"score":0.35280001163482666},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.337799996137619},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33719998598098755},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33570000529289246},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.319599986076355},{"id":"https://openalex.org/C34320192","wikidata":"https://www.wikidata.org/wiki/Q783105","display_name":"Linear complementarity problem","level":3,"score":0.30230000615119934},{"id":"https://openalex.org/C166077713","wikidata":"https://www.wikidata.org/wiki/Q1758924","display_name":"Tensor field","level":3,"score":0.26589998602867126},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.257099986076355},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.2565999925136566}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10957-026-03061-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-026-03061-8","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6212025128","display_name":"\u7edd\u5bf9\u503c\u65b9\u7a0b\u7ec4\u7684\u5feb\u901f\u8fed\u4ee3\u7b97\u6cd5\u53ca\u5176\u5728\u4e92\u8865\u95ee\u9898\u4e2d\u7684\u5e94\u7528\u7814\u7a76","funder_award_id":"11961082","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W175892734","https://openalex.org/W1912937193","https://openalex.org/W2037934905","https://openalex.org/W2133937084","https://openalex.org/W2204354727","https://openalex.org/W2266798071","https://openalex.org/W2566270643","https://openalex.org/W2781896505","https://openalex.org/W2783122985","https://openalex.org/W2794288744","https://openalex.org/W2806432822","https://openalex.org/W2886917779","https://openalex.org/W2946480664","https://openalex.org/W2962705706","https://openalex.org/W2963018695","https://openalex.org/W2966845367","https://openalex.org/W2967514193","https://openalex.org/W2968579382","https://openalex.org/W2982075509","https://openalex.org/W2992546123","https://openalex.org/W3006636766","https://openalex.org/W3195466780","https://openalex.org/W3217515895","https://openalex.org/W4210568647","https://openalex.org/W4210957680","https://openalex.org/W4226401466","https://openalex.org/W4296690015","https://openalex.org/W4313268854","https://openalex.org/W4321186279","https://openalex.org/W4383721075","https://openalex.org/W4390650824","https://openalex.org/W4390662288","https://openalex.org/W4391034913","https://openalex.org/W4394603798","https://openalex.org/W4398764236","https://openalex.org/W4401900192","https://openalex.org/W4403742545","https://openalex.org/W4405764597","https://openalex.org/W4407363138","https://openalex.org/W4408010173","https://openalex.org/W4410758972","https://openalex.org/W4411370803","https://openalex.org/W4411499255","https://openalex.org/W4411546559","https://openalex.org/W4413181557"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2026-07-18T00:00:00"}
