{"id":"https://openalex.org/W3209541907","doi":"https://doi.org/10.1007/s10957-021-01963-3","title":"Evolutionary Quasi-Variational-Hemivariational Inequalities I: Existence and Optimal Control","display_name":"Evolutionary Quasi-Variational-Hemivariational Inequalities I: Existence and Optimal Control","publication_year":2021,"publication_date":"2021-11-02","ids":{"openalex":"https://openalex.org/W3209541907","doi":"https://doi.org/10.1007/s10957-021-01963-3","mag":"3209541907"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-021-01963-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-021-01963-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-021-01963-3.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10957-021-01963-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028260946","display_name":"Shengda Zeng","orcid":"https://orcid.org/0000-0003-1818-842X"},"institutions":[{"id":"https://openalex.org/I27462735","display_name":"Yulin Normal University","ror":"https://ror.org/00445hv47","country_code":"CN","type":"education","lineage":["https://openalex.org/I27462735"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shengda Zeng","raw_affiliation_strings":["Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, 537000, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, 537000, People's Republic of China","institution_ids":["https://openalex.org/I27462735"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007418841","display_name":"Dumitru Motreanu","orcid":"https://orcid.org/0000-0001-7391-9534"},"institutions":[{"id":"https://openalex.org/I27462735","display_name":"Yulin Normal University","ror":"https://ror.org/00445hv47","country_code":"CN","type":"education","lineage":["https://openalex.org/I27462735"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dumitru Motreanu","raw_affiliation_strings":["College of Science, Yulin Normal University, Yulin, Guangxi, 537000, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Yulin Normal University, Yulin, Guangxi, 537000, People's Republic of China","institution_ids":["https://openalex.org/I27462735"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013676704","display_name":"Akhtar A. Khan","orcid":"https://orcid.org/0000-0002-8229-6604"},"institutions":[{"id":"https://openalex.org/I155173764","display_name":"Rochester Institute of Technology","ror":"https://ror.org/00v4yb702","country_code":"US","type":"education","lineage":["https://openalex.org/I155173764"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Akhtar A. Khan","raw_affiliation_strings":["School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York, 14623, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York, 14623, USA","institution_ids":["https://openalex.org/I155173764"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5028260946"],"corresponding_institution_ids":["https://openalex.org/I27462735"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":2.5871,"has_fulltext":true,"cited_by_count":23,"citation_normalized_percentile":{"value":0.91108779,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"193","issue":"1-3","first_page":"950","last_page":"970"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9998999834060669,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9998999834060669,"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/T11115","display_name":"Topology Optimization in Engineering","score":0.991599977016449,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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":0.9886000156402588,"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/mathematics","display_name":"Mathematics","score":0.9080218076705933},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.6757566332817078},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5947827100753784},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5885499119758606},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.5733051896095276},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.5692777037620544},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5173751711845398},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5067756772041321},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.49548280239105225},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48083218932151794},{"id":"https://openalex.org/keywords/existence-theorem","display_name":"Existence theorem","score":0.4612520933151245},{"id":"https://openalex.org/keywords/solution-set","display_name":"Solution set","score":0.4424769878387451},{"id":"https://openalex.org/keywords/variational-analysis","display_name":"Variational analysis","score":0.42099589109420776},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.38035497069358826},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33223000168800354},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3181826174259186},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08255314826965332}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9080218076705933},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.6757566332817078},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5947827100753784},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5885499119758606},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.5733051896095276},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.5692777037620544},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5173751711845398},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5067756772041321},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.49548280239105225},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48083218932151794},{"id":"https://openalex.org/C2776548862","wikidata":"https://www.wikidata.org/wiki/Q2694495","display_name":"Existence theorem","level":2,"score":0.4612520933151245},{"id":"https://openalex.org/C60033838","wikidata":"https://www.wikidata.org/wiki/Q1751685","display_name":"Solution set","level":3,"score":0.4424769878387451},{"id":"https://openalex.org/C523394659","wikidata":"https://www.wikidata.org/wiki/Q17086892","display_name":"Variational analysis","level":2,"score":0.42099589109420776},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.38035497069358826},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33223000168800354},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3181826174259186},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08255314826965332},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10957-021-01963-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-021-01963-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-021-01963-3.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04791782v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04791782","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Optimization Theory and Applications, 2021, 193 (1-3), pp.950-970. &#x27E8;10.1007/s10957-021-01963-3&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:RePEc:spr:joptap:v:193:y:2022:i:1:d:10.1007_s10957-021-01963-3","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-021-01963-3","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10957-021-01963-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-021-01963-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-021-01963-3.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5799999833106995,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G1648256697","display_name":null,"funder_award_id":"823731","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G1942756822","display_name":null,"funder_award_id":"12026255","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2031092425","display_name":null,"funder_award_id":"823731 CONMECH","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G2295935453","display_name":null,"funder_award_id":"823731 CONMECH","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2833540710","display_name":null,"funder_award_id":"823731","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4027647712","display_name":null,"funder_award_id":"1720067","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4268872271","display_name":null,"funder_award_id":"12026256","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G461778075","display_name":null,"funder_award_id":"G2020ZK07","funder_id":"https://openalex.org/F4320329507","funder_display_name":"Yulin Normal University"},{"id":"https://openalex.org/G4790121765","display_name":null,"funder_award_id":"440328/PnH2/2019","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4902843723","display_name":null,"funder_award_id":"12001478","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4937468798","display_name":null,"funder_award_id":"H2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5848258319","display_name":null,"funder_award_id":"0 and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7842005466","display_name":null,"funder_award_id":"Horizon 2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G902325810","display_name":null,"funder_award_id":"823731","funder_id":"https://openalex.org/F4320335254","funder_display_name":"Horizon 2020"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320329507","display_name":"Yulin Normal University","ror":"https://ror.org/00445hv47"},{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320335254","display_name":"Horizon 2020","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3209541907.pdf","grobid_xml":"https://content.openalex.org/works/W3209541907.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W576238630","https://openalex.org/W641727423","https://openalex.org/W941550432","https://openalex.org/W1234695500","https://openalex.org/W1545761024","https://openalex.org/W1547403762","https://openalex.org/W1551360398","https://openalex.org/W1924182126","https://openalex.org/W1971981743","https://openalex.org/W1973096185","https://openalex.org/W1974332228","https://openalex.org/W1983730159","https://openalex.org/W1984383625","https://openalex.org/W2007225098","https://openalex.org/W2016362012","https://openalex.org/W2019821278","https://openalex.org/W2020717540","https://openalex.org/W2041603593","https://openalex.org/W2055578548","https://openalex.org/W2056390735","https://openalex.org/W2074629902","https://openalex.org/W2079002248","https://openalex.org/W2084845949","https://openalex.org/W2092196160","https://openalex.org/W2092532386","https://openalex.org/W2149198107","https://openalex.org/W2238943295","https://openalex.org/W2342810421","https://openalex.org/W2484453099","https://openalex.org/W2493323244","https://openalex.org/W2494236341","https://openalex.org/W2582171088","https://openalex.org/W2596534281","https://openalex.org/W2632133090","https://openalex.org/W2740013339","https://openalex.org/W2767056423","https://openalex.org/W2774372052","https://openalex.org/W2791104169","https://openalex.org/W2896380383","https://openalex.org/W2909065560","https://openalex.org/W2943791922","https://openalex.org/W2973981673","https://openalex.org/W2996861704","https://openalex.org/W3099364443","https://openalex.org/W4214771318","https://openalex.org/W4237844826","https://openalex.org/W4248253146","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2142789187","https://openalex.org/W1967128235","https://openalex.org/W1561544985","https://openalex.org/W1992673508","https://openalex.org/W1990596250","https://openalex.org/W2096585912","https://openalex.org/W2116234265","https://openalex.org/W2055511209","https://openalex.org/W2024950195","https://openalex.org/W2026306944"],"abstract_inverted_index":{"Abstract":[0],"We":[1,37,96],"study":[2],"a":[3,12,25,31,48],"nonlinear":[4],"evolutionary":[5],"quasi\u2013variational\u2013hemivariational":[6],"inequality":[7],"(in":[8],"short,":[9],"(QVHVI))":[10],"involving":[11],"set-valued":[13,81],"pseudo-monotone":[14],"map.":[15],"The":[16],"central":[17],"idea":[18],"of":[19,23,41,54,100,112],"our":[20],"approach":[21],"consists":[22],"introducing":[24],"parametric":[26,43],"variational":[27,32,44],"problem":[28,45,90,106],"that":[29],"defines":[30],"selection":[33],"associated":[34],"with":[35,57],"(QVHVI).":[36],"prove":[38,97],"the":[39,42,52,63,92,98,103,108,113,117,122],"solvability":[40],"by":[46,74],"employing":[47],"surjectivity":[49],"theorem":[50,69,79,120],"for":[51,70,80,91,102],"sum":[53],"operators,":[55],"combined":[56],"Minty\u2019s":[58],"formulation":[59],"and":[60,107,121],"techniques":[61],"from":[62],"nonsmooth":[64],"analysis.":[65],"Then,":[66],"an":[67,84,86],"existence":[68,99],"(QVHVI)":[71,93],"is":[72,94],"established":[73],"using":[75],"Kluge\u2019s":[76],"fixed":[77],"point":[78],"operators.":[82],"As":[83],"application,":[85],"abstract":[87],"optimal":[88,104],"control":[89,105],"investigated.":[95],"solutions":[101],"weak":[109],"sequential":[110],"compactness":[111],"solution":[114],"set":[115],"via":[116],"Weierstrass":[118],"minimization":[119],"Kuratowski-type":[123],"continuity":[124],"properties.":[125]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2}],"updated_date":"2026-05-20T08:49:12.498775","created_date":"2025-10-10T00:00:00"}
