{"id":"https://openalex.org/W4205449078","doi":"https://doi.org/10.3390/sym14020199","title":"The Optimal Control Problems for Generalized Elliptic Quasivariational Inequalities","display_name":"The Optimal Control Problems for Generalized Elliptic Quasivariational Inequalities","publication_year":2022,"publication_date":"2022-01-20","ids":{"openalex":"https://openalex.org/W4205449078","doi":"https://doi.org/10.3390/sym14020199"},"language":"en","primary_location":{"id":"doi:10.3390/sym14020199","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14020199","pdf_url":"https://www.mdpi.com/2073-8994/14/2/199/pdf?version=1642666929","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/2/199/pdf?version=1642666929","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102157579","display_name":"Shih-sen Chang","orcid":null},"institutions":[{"id":"https://openalex.org/I184693016","display_name":"China Medical University","ror":"https://ror.org/00v408z34","country_code":"TW","type":"education","lineage":["https://openalex.org/I184693016"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Shih-Sen Chang","raw_affiliation_strings":["Center for General Education, China Medical University, Taichung 40402, Taiwan"],"affiliations":[{"raw_affiliation_string":"Center for General Education, China Medical University, Taichung 40402, Taiwan","institution_ids":["https://openalex.org/I184693016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074498692","display_name":"Abdullah Ali H. Ahmadini","orcid":"https://orcid.org/0000-0002-9740-7207"},"institutions":[{"id":"https://openalex.org/I91450128","display_name":"Jazan University","ror":"https://ror.org/02bjnq803","country_code":"SA","type":"education","lineage":["https://openalex.org/I91450128"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Abdullah Ali H. Ahmadini","raw_affiliation_strings":["Department of Mathematics, Jazan University, Jazan 45142, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Jazan University, Jazan 45142, Saudi Arabia","institution_ids":["https://openalex.org/I91450128"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035737050","display_name":"Salahuddin Salahuddin","orcid":null},"institutions":[{"id":"https://openalex.org/I91450128","display_name":"Jazan University","ror":"https://ror.org/02bjnq803","country_code":"SA","type":"education","lineage":["https://openalex.org/I91450128"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Salahuddin","raw_affiliation_strings":["Department of Mathematics, Jazan University, Jazan 45142, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Jazan University, Jazan 45142, Saudi Arabia","institution_ids":["https://openalex.org/I91450128"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101475946","display_name":"Min Liu","orcid":"https://orcid.org/0000-0002-4952-2577"},"institutions":[{"id":"https://openalex.org/I4210131342","display_name":"Yibin University","ror":"https://ror.org/03w8m2977","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210131342"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Min Liu","raw_affiliation_strings":["Department of Mathematics, Yibin University, Yibin 644007, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yibin University, Yibin 644007, China","institution_ids":["https://openalex.org/I4210131342"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028793940","display_name":"Jinfang Tang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210131342","display_name":"Yibin University","ror":"https://ror.org/03w8m2977","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210131342"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinfang Tang","raw_affiliation_strings":["Department of Mathematics, Yibin University, Yibin 644007, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yibin University, Yibin 644007, China","institution_ids":["https://openalex.org/I4210131342"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5102157579"],"corresponding_institution_ids":["https://openalex.org/I184693016"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.5842,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.67565834,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"14","issue":"2","first_page":"199","last_page":"199"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":1.0,"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":1.0,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9937999844551086,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.723811149597168},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7115986347198486},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.697945773601532},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6964783072471619},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6471667289733887},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5801113843917847},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.5219920873641968},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5207957625389099},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.44180259108543396},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.43884438276290894},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.4171485900878906},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40917032957077026},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24673643708229065},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2004060447216034}],"concepts":[{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.723811149597168},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7115986347198486},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.697945773601532},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6964783072471619},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6471667289733887},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5801113843917847},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.5219920873641968},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5207957625389099},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.44180259108543396},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.43884438276290894},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.4171485900878906},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40917032957077026},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24673643708229065},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2004060447216034},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14020199","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14020199","pdf_url":"https://www.mdpi.com/2073-8994/14/2/199/pdf?version=1642666929","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:451cf1e13c9e4feea42c558c03b52a8f","is_oa":true,"landing_page_url":"https://doaj.org/article/451cf1e13c9e4feea42c558c03b52a8f","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 2, p 199 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/2/199/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14020199","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14020199","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14020199","pdf_url":"https://www.mdpi.com/2073-8994/14/2/199/pdf?version=1642666929","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5799999833106995}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4205449078.pdf","grobid_xml":"https://content.openalex.org/works/W4205449078.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W34508408","https://openalex.org/W606079047","https://openalex.org/W1490112587","https://openalex.org/W1545761024","https://openalex.org/W1966546278","https://openalex.org/W1990759037","https://openalex.org/W2032668029","https://openalex.org/W2036568403","https://openalex.org/W2044751485","https://openalex.org/W2046369964","https://openalex.org/W2101340781","https://openalex.org/W2120757254","https://openalex.org/W2484453099","https://openalex.org/W2588144790","https://openalex.org/W2601098399","https://openalex.org/W2612069296","https://openalex.org/W2616991700","https://openalex.org/W2738446416","https://openalex.org/W2804565623","https://openalex.org/W2904524187","https://openalex.org/W2922185639","https://openalex.org/W3026897652","https://openalex.org/W3036003430","https://openalex.org/W3045059237","https://openalex.org/W3083449804","https://openalex.org/W3098158480","https://openalex.org/W3116233867","https://openalex.org/W3119330394","https://openalex.org/W3159417296","https://openalex.org/W3211464162","https://openalex.org/W4214498954","https://openalex.org/W4234028290","https://openalex.org/W4292311687"],"related_works":["https://openalex.org/W2487640660","https://openalex.org/W2612526717","https://openalex.org/W2121543990","https://openalex.org/W2402800040","https://openalex.org/W4252969132","https://openalex.org/W2000020320","https://openalex.org/W2805799113","https://openalex.org/W4394650907","https://openalex.org/W1981078319","https://openalex.org/W3118444755"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3,18,62],"propose":[4],"an":[5,60],"optimal":[6,32,72],"control":[7,33,73],"problem":[8],"for":[9,41],"generalized":[10,42],"elliptic":[11,43],"quasi-variational":[12,44],"inequality":[13],"with":[14,75],"unilateral":[15],"constraints.":[16],"Then,":[17],"discuss":[19],"the":[20,25,28,31,48,64,69],"sufficient":[21],"assumptions":[22],"that":[23],"ensure":[24],"convergence":[26,39,66],"of":[27,50,71],"solutions":[29],"to":[30],"problem.":[34],"The":[35],"proofs":[36],"depend":[37],"on":[38],"results":[40,67],"inequalities,":[45],"obtained":[46],"by":[47],"arguments":[49],"compactness,":[51],"lower":[52],"semi-continuity,":[53],"monotonicity,":[54],"penalty":[55],"and":[56],"different":[57],"estimates.":[58],"As":[59],"application,":[61],"addressed":[63],"abstract":[65],"in":[68],"analysis":[70],"associated":[74],"boundary":[76],"value":[77],"problems.":[78]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}