{"id":"https://openalex.org/W2980805366","doi":"https://doi.org/10.3390/math7100974","title":"Weighted Method for Uncertain Nonlinear Variational Inequality Problems","display_name":"Weighted Method for Uncertain Nonlinear Variational Inequality Problems","publication_year":2019,"publication_date":"2019-10-15","ids":{"openalex":"https://openalex.org/W2980805366","doi":"https://doi.org/10.3390/math7100974","mag":"2980805366"},"language":"en","primary_location":{"id":"doi:10.3390/math7100974","doi":"https://doi.org/10.3390/math7100974","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math7100974","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"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":"Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/math7100974","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077899928","display_name":"Cunlin Li","orcid":"https://orcid.org/0000-0002-0272-1210","observed_orcids":["https://orcid.org/0000-0002-0272-1210"]},"institutions":[{"id":"https://openalex.org/I3019309368","display_name":"North Minzu University","ror":"https://ror.org/05xjevr11","country_code":"CN","type":"education","lineage":["https://openalex.org/I3019309368"]},{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Cunlin Li","raw_affiliation_strings":["Ningxia Key Laboratory of Intelligent Information and Big Data Processing, Governance and Social Management Research Center of Northwest Ethnic Regions, North Minzu University, Yinchuan 750021, China","School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China","State Key Laboratory of Mechanics Control of Mechanical Structures, Institute of Nano Science and Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"],"raw_orcid":"https://orcid.org/0000-0002-0272-1210","affiliations":[{"raw_affiliation_string":"Ningxia Key Laboratory of Intelligent Information and Big Data Processing, Governance and Social Management Research Center of Northwest Ethnic Regions, North Minzu University, Yinchuan 750021, China","institution_ids":["https://openalex.org/I3019309368"]},{"raw_affiliation_string":"School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China","institution_ids":["https://openalex.org/I3019309368"]},{"raw_affiliation_string":"State Key Laboratory of Mechanics Control of Mechanical Structures, Institute of Nano Science and Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004206649","display_name":"Mihai Postolache","orcid":"https://orcid.org/0000-0003-0738-787X","observed_orcids":["https://orcid.org/0000-0003-0738-787X"]},"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"]},{"id":"https://openalex.org/I58077936","display_name":"Romanian Academy","ror":"https://ror.org/0561n6946","country_code":"RO","type":"archive","lineage":["https://openalex.org/I58077936"]},{"id":"https://openalex.org/I61641377","display_name":"Universitatea Na\u021bional\u0103 de \u0218tiin\u021b\u0103 \u0219i Tehnologie Politehnica Bucure\u0219ti","ror":"https://ror.org/0558j5q12","country_code":"RO","type":"education","lineage":["https://openalex.org/I61641377"]}],"countries":["RO","TW"],"is_corresponding":true,"raw_author_name":"Mihai Postolache","raw_affiliation_strings":["Center for General Education, China Medical University, Taichung 40402, Taiwan","Department of Mathematics and Informatics, University \u201cPolitehnica\u201d of Bucharest, 060042 Bucharest, Romania","Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, 050711 Bucharest, Romania"],"raw_orcid":"https://orcid.org/0000-0003-0738-787X","affiliations":[{"raw_affiliation_string":"Center for General Education, China Medical University, Taichung 40402, Taiwan","institution_ids":["https://openalex.org/I184693016"]},{"raw_affiliation_string":"Department of Mathematics and Informatics, University \u201cPolitehnica\u201d of Bucharest, 060042 Bucharest, Romania","institution_ids":["https://openalex.org/I61641377"]},{"raw_affiliation_string":"Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, 050711 Bucharest, Romania","institution_ids":["https://openalex.org/I58077936"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038920344","display_name":"Zhifu Jia","orcid":"https://orcid.org/0000-0001-8287-3208","observed_orcids":["https://orcid.org/0000-0001-8287-3208"]},"institutions":[{"id":"https://openalex.org/I3019309368","display_name":"North Minzu University","ror":"https://ror.org/05xjevr11","country_code":"CN","type":"education","lineage":["https://openalex.org/I3019309368"]},{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhifu Jia","raw_affiliation_strings":["School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China","State Key Laboratory of Mechanics Control of Mechanical Structures, Institute of Nano Science and Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"],"raw_orcid":"https://orcid.org/0000-0001-8287-3208","affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China","institution_ids":["https://openalex.org/I3019309368"]},{"raw_affiliation_string":"State Key Laboratory of Mechanics Control of Mechanical Structures, Institute of Nano Science and Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China","institution_ids":["https://openalex.org/I9842412"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5004206649"],"corresponding_institution_ids":["https://openalex.org/I184693016","https://openalex.org/I58077936","https://openalex.org/I61641377"],"apc_list":{"value":1200,"currency":"CHF","value_usd":1216},"apc_paid":{"value":1200,"currency":"CHF","value_usd":1216},"fwci":0.3396,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.58056552,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":96},"biblio":{"volume":"7","issue":"10","first_page":"974","last_page":"974"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9003999829292297,"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":0.9003999829292297,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.09160000085830688,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.0026000000070780516,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/uncertain-variables","display_name":"uncertain variables","score":0.8270000219345093},{"id":"https://openalex.org/keywords/gap-function","display_name":"gap function","score":0.6230000257492065},{"id":"https://openalex.org/keywords/convergence-analysis","display_name":"convergence analysis","score":0.7609999775886536},{"id":"https://openalex.org/keywords/holder-continuity","display_name":"H\u00f6lder continuity","score":0.8059999942779541},{"id":"https://openalex.org/keywords/asymptotic-behavior","display_name":"asymptotic behavior","score":0.45899999141693115}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6948471069335938},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6691840887069702},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.6640845537185669},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6151725053787231},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5983222723007202},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.5830457210540771},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5618476271629333},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46662700176239014},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.4577130675315857},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45125612616539},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.417263388633728},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15608695149421692},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.09950709342956543},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.059324949979782104},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/math7100974","doi":"https://doi.org/10.3390/math7100974","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math7100974","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"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":"Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:gam:jmathe:v:7:y:2019:i:10:p:974-:d:276637","doi":null,"is_oa":false,"landing_page_url":"https://www.mdpi.com/2227-7390/7/10/974/","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,"listed_in":[],"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"},{"id":"pmh:oai:doaj.org/article:f4375841783a4873904e6b43f9bd7908","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/f4375841783a4873904e6b43f9bd7908","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics, Vol 7, Iss 10, p 974 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/math7100974","doi":"https://doi.org/10.3390/math7100974","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math7100974","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"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":"Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2233657660","display_name":"\u4e0d\u786e\u5b9a\u4fe1\u606f\u6761\u4ef6\u4e0b\u7684\u535a\u5f08\u5efa\u6a21\u53ca\u6700\u4f18\u7b56\u7565\u7814\u7a76","funder_award_id":"71561001","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":15,"referenced_works":["https://openalex.org/W7585563","https://openalex.org/W1007193218","https://openalex.org/W1543439990","https://openalex.org/W1754906513","https://openalex.org/W1985348591","https://openalex.org/W2019088302","https://openalex.org/W2045813298","https://openalex.org/W2076897083","https://openalex.org/W2098650062","https://openalex.org/W2149918912","https://openalex.org/W2591631865","https://openalex.org/W2616444305","https://openalex.org/W2769972669","https://openalex.org/W4236577982","https://openalex.org/W4300580367"],"related_works":["https://openalex.org/W2769972669","https://openalex.org/W1612593628","https://openalex.org/W4365510345","https://openalex.org/W4380086324","https://openalex.org/W1007193218","https://openalex.org/W1248890587","https://openalex.org/W4200605164","https://openalex.org/W7212778655","https://openalex.org/W2216639753","https://openalex.org/W2030317353"],"abstract_inverted_index":{"A":[0],"convex":[1],"combined":[2],"expectations":[3],"regularized":[4],"gap":[5],"function":[6],"with":[7,14],"uncertain":[8,15,31,46,66,87],"variable":[9],"is":[10,23,52,82,105],"presented":[11],"to":[12],"deal":[13],"nonlinear":[16],"variational":[17],"inequality":[18],"problems":[19],"(UNVIP).":[20],"The":[21,68],"UNVIP":[22],"transformed":[24,73],"into":[25],"a":[26,78],"minimization":[27,50],"problem":[28],"through":[29,54],"an":[30],"weighted":[32,47],"expected":[33,48],"residual":[34,49],"function.":[35],"Moreover,":[36],"the":[37,40,45,55,61,65,72,85,93,101,108],"convergence":[38,94],"of":[39,44,64,71,92,95,110],"global":[41],"optimal":[42],"solutions":[43],"model":[51,74,97],"given":[53],"integration":[56],"by":[57],"parts":[58],"method":[59,81,104],"under":[60,107],"compact":[62,79,102],"space":[63],"event.":[67],"limiting":[69],"behaviors":[70],"are":[75],"analyzed.":[76],"Furthermore,":[77],"approximation":[80,103],"proposed":[83],"in":[84],"unbounded":[86],"event":[88],"space.":[89],"Through":[90],"analysis":[91],"UWERM":[96],"and":[98],"reasonable":[99],"hypothesis,":[100],"verified":[106],"circumstance":[109],"Holder":[111],"continuity.":[112]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2019-10-25T00:00:00"}