{"id":"https://openalex.org/W7154606430","doi":"https://doi.org/10.1007/s10957-026-02982-8","title":"A System of Differential Inverse Mixed Variational Inequalities: Existence, Uniqueness, and Algorithm","display_name":"A System of Differential Inverse Mixed Variational Inequalities: Existence, Uniqueness, and Algorithm","publication_year":2026,"publication_date":"2026-04-16","ids":{"openalex":"https://openalex.org/W7154606430","doi":"https://doi.org/10.1007/s10957-026-02982-8"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-026-02982-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-026-02982-8","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/A5110096575","display_name":"Zhang Huang","orcid":"https://orcid.org/0009-0002-1687-5461"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]},{"id":"https://openalex.org/I24201400","display_name":"Chengdu University of Information Technology","ror":"https://ror.org/01yxwrh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I24201400"]},{"id":"https://openalex.org/I31595395","display_name":"Chengdu University of Technology","ror":"https://ror.org/05pejbw21","country_code":"CN","type":"education","lineage":["https://openalex.org/I31595395"]},{"id":"https://openalex.org/I4210125143","display_name":"Chengdu University","ror":"https://ror.org/034z67559","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210125143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang Huang","raw_affiliation_strings":["School of Mathematical Sciences, Chengdu University of Technology, Chengdu, Sichuan, 610059, P.R. China"],"raw_orcid":"https://orcid.org/0009-0002-1687-5461","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Chengdu University of Technology, Chengdu, Sichuan, 610059, P.R. China","institution_ids":["https://openalex.org/I31595395","https://openalex.org/I24201400","https://openalex.org/I150229711","https://openalex.org/I4210125143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100371213","display_name":"Weiwei Li","orcid":"https://orcid.org/0000-0002-7329-4236"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]},{"id":"https://openalex.org/I24201400","display_name":"Chengdu University of Information Technology","ror":"https://ror.org/01yxwrh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I24201400"]},{"id":"https://openalex.org/I31595395","display_name":"Chengdu University of Technology","ror":"https://ror.org/05pejbw21","country_code":"CN","type":"education","lineage":["https://openalex.org/I31595395"]},{"id":"https://openalex.org/I4210125143","display_name":"Chengdu University","ror":"https://ror.org/034z67559","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210125143"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wei Li","raw_affiliation_strings":["School of Mathematical Sciences, Chengdu University of Technology, Chengdu, Sichuan, 610059, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Chengdu University of Technology, Chengdu, Sichuan, 610059, P.R. China","institution_ids":["https://openalex.org/I31595395","https://openalex.org/I24201400","https://openalex.org/I150229711","https://openalex.org/I4210125143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030927091","display_name":"Q Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]},{"id":"https://openalex.org/I24201400","display_name":"Chengdu University of Information Technology","ror":"https://ror.org/01yxwrh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I24201400"]},{"id":"https://openalex.org/I31595395","display_name":"Chengdu University of Technology","ror":"https://ror.org/05pejbw21","country_code":"CN","type":"education","lineage":["https://openalex.org/I31595395"]},{"id":"https://openalex.org/I4210125143","display_name":"Chengdu University","ror":"https://ror.org/034z67559","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210125143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qixia Zhang","raw_affiliation_strings":["School of Mathematical Sciences, Chengdu University of Technology, Chengdu, Sichuan, 610059, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Chengdu University of Technology, Chengdu, Sichuan, 610059, P.R. China","institution_ids":["https://openalex.org/I31595395","https://openalex.org/I24201400","https://openalex.org/I150229711","https://openalex.org/I4210125143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133781806","display_name":"Jieke Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]},{"id":"https://openalex.org/I24201400","display_name":"Chengdu University of Information Technology","ror":"https://ror.org/01yxwrh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I24201400"]},{"id":"https://openalex.org/I31595395","display_name":"Chengdu University of Technology","ror":"https://ror.org/05pejbw21","country_code":"CN","type":"education","lineage":["https://openalex.org/I31595395"]},{"id":"https://openalex.org/I4210125143","display_name":"Chengdu University","ror":"https://ror.org/034z67559","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210125143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jieke Xu","raw_affiliation_strings":["School of Mathematical Sciences, Chengdu University of Technology, Chengdu, Sichuan, 610059, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Chengdu University of Technology, Chengdu, Sichuan, 610059, P.R. China","institution_ids":["https://openalex.org/I31595395","https://openalex.org/I24201400","https://openalex.org/I150229711","https://openalex.org/I4210125143"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011209445","display_name":"Chunyan Yang","orcid":"https://orcid.org/0009-0006-0426-9244"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chunyan Yang","raw_affiliation_strings":["Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610065, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610065, P.R. China","institution_ids":["https://openalex.org/I24185976"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5100371213"],"corresponding_institution_ids":["https://openalex.org/I150229711","https://openalex.org/I24201400","https://openalex.org/I31595395","https://openalex.org/I4210125143"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.41603834,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"209","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10524","display_name":"Traffic control and management","score":0.7817999720573425,"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"}},"topics":[{"id":"https://openalex.org/T10524","display_name":"Traffic control and management","score":0.7817999720573425,"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":0.12919999659061432,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.012400000356137753,"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/variational-inequality","display_name":"Variational inequality","score":0.7504000067710876},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5723999738693237},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.5189999938011169},{"id":"https://openalex.org/keywords/differential-inclusion","display_name":"Differential inclusion","score":0.482699990272522},{"id":"https://openalex.org/keywords/projected-dynamical-system","display_name":"Projected dynamical system","score":0.4449000060558319},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.42179998755455017},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.4090000092983246},{"id":"https://openalex.org/keywords/variational-analysis","display_name":"Variational analysis","score":0.40310001373291016}],"concepts":[{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.7504000067710876},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7304999828338623},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5723999738693237},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.5189999938011169},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49869999289512634},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.482699990272522},{"id":"https://openalex.org/C93812963","wikidata":"https://www.wikidata.org/wiki/Q7249433","display_name":"Projected dynamical system","level":5,"score":0.4449000060558319},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.42179998755455017},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4090000092983246},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4074999988079071},{"id":"https://openalex.org/C523394659","wikidata":"https://www.wikidata.org/wiki/Q17086892","display_name":"Variational analysis","level":2,"score":0.40310001373291016},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.38909998536109924},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.3709000051021576},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.36329999566078186},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.3310999870300293},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.3107999861240387},{"id":"https://openalex.org/C52154503","wikidata":"https://www.wikidata.org/wiki/Q7915797","display_name":"Variational integrator","level":4,"score":0.30480000376701355},{"id":"https://openalex.org/C207512268","wikidata":"https://www.wikidata.org/wiki/Q3074551","display_name":"Traffic flow (computer networking)","level":2,"score":0.29420000314712524},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.2825999855995178},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28189998865127563},{"id":"https://openalex.org/C205269179","wikidata":"https://www.wikidata.org/wiki/Q17144160","display_name":"Microscopic traffic flow model","level":3,"score":0.28060001134872437},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C64618476","wikidata":"https://www.wikidata.org/wiki/Q164296","display_name":"Variational method","level":2,"score":0.2551000118255615},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10957-026-02982-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-026-02982-8","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/G7238814065","display_name":null,"funder_award_id":"12301395","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1975858012","https://openalex.org/W1976674821","https://openalex.org/W1978275886","https://openalex.org/W1980909723","https://openalex.org/W1981981726","https://openalex.org/W1982267238","https://openalex.org/W1982897003","https://openalex.org/W1983186081","https://openalex.org/W2018730376","https://openalex.org/W2046899605","https://openalex.org/W2050517827","https://openalex.org/W2065106598","https://openalex.org/W2108678875","https://openalex.org/W2109783572","https://openalex.org/W2155312546","https://openalex.org/W2228195434","https://openalex.org/W2260520465","https://openalex.org/W2328285789","https://openalex.org/W2598465882","https://openalex.org/W2936535340","https://openalex.org/W3121412662","https://openalex.org/W3194371901","https://openalex.org/W4251507077","https://openalex.org/W4284679551","https://openalex.org/W4324395142","https://openalex.org/W4387363917","https://openalex.org/W4388714136","https://openalex.org/W4388843795","https://openalex.org/W4391746518","https://openalex.org/W4394811662","https://openalex.org/W4394842060","https://openalex.org/W4402874656","https://openalex.org/W4411170461"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-17T06:04:52.305304","created_date":"2026-04-17T00:00:00"}