{"id":"https://openalex.org/W2122111521","doi":"https://doi.org/10.1109/ijcnn.2008.4633774","title":"A simplified recurrent neural network for solving nonlinear variational inequalities","display_name":"A simplified recurrent neural network for solving nonlinear variational inequalities","publication_year":2008,"publication_date":"2008-06-01","ids":{"openalex":"https://openalex.org/W2122111521","doi":"https://doi.org/10.1109/ijcnn.2008.4633774","mag":"2122111521"},"language":"en","primary_location":{"id":"doi:10.1109/ijcnn.2008.4633774","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2008.4633774","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence)","raw_type":"proceedings-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/A5108401200","display_name":"Long Cheng","orcid":"https://orcid.org/0000-0001-7565-8788"},"institutions":[{"id":"https://openalex.org/I4210094879","display_name":"Shandong Institute of Automation","ror":"https://ror.org/00qdtba35","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210094879","https://openalex.org/I4210142748"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Long Cheng","raw_affiliation_strings":["Key Laboratory of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy and Sciences, Beijing, China","Key Lab. of Complex Syst. & Intell. Sci., Chinese Acad. of Sci., Beijing"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy and Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210094879"]},{"raw_affiliation_string":"Key Lab. of Complex Syst. & Intell. Sci., Chinese Acad. of Sci., Beijing","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109333020","display_name":"Zeng\u2010Guang Hou","orcid":"https://orcid.org/0000-0002-1534-5840"},"institutions":[{"id":"https://openalex.org/I4210094879","display_name":"Shandong Institute of Automation","ror":"https://ror.org/00qdtba35","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210094879","https://openalex.org/I4210142748"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zeng-Guang Hou","raw_affiliation_strings":["Key Laboratory of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy and Sciences, Beijing, China","Key Lab. of Complex Syst. & Intell. Sci., Chinese Acad. of Sci., Beijing"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy and Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210094879"]},{"raw_affiliation_string":"Key Lab. of Complex Syst. & Intell. Sci., Chinese Acad. of Sci., Beijing","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024708104","display_name":"Min Tan","orcid":"https://orcid.org/0000-0002-1986-8438"},"institutions":[{"id":"https://openalex.org/I4210094879","display_name":"Shandong Institute of Automation","ror":"https://ror.org/00qdtba35","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210094879","https://openalex.org/I4210142748"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Min Tan","raw_affiliation_strings":["Key Laboratory of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy and Sciences, Beijing, China","Key Lab. of Complex Syst. & Intell. Sci., Chinese Acad. of Sci., Beijing"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy and Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210094879"]},{"raw_affiliation_string":"Key Lab. of Complex Syst. & Intell. Sci., Chinese Acad. of Sci., Beijing","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101667821","display_name":"Xiuqing Wang","orcid":"https://orcid.org/0000-0003-1723-3583"},"institutions":[{"id":"https://openalex.org/I94611258","display_name":"Hebei Normal University","ror":"https://ror.org/004rbbw49","country_code":"CN","type":"education","lineage":["https://openalex.org/I94611258"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiuqing Wang","raw_affiliation_strings":["Vocational & Technical Institute, Hebei Normal University, Shijiazhuang, China","Vocational&Tech. Inst., Hebei Normal Univ., Shijiazhuang"],"affiliations":[{"raw_affiliation_string":"Vocational & Technical Institute, Hebei Normal University, Shijiazhuang, China","institution_ids":["https://openalex.org/I94611258"]},{"raw_affiliation_string":"Vocational&Tech. Inst., Hebei Normal Univ., Shijiazhuang","institution_ids":["https://openalex.org/I94611258"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5108401200"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210094879"],"apc_list":null,"apc_paid":null,"fwci":1.1441,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.84581567,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"104","last_page":"109"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9864000082015991,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10320","display_name":"Neural Networks and Applications","score":0.9864000082015991,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T13579","display_name":"Image and Video Stabilization","score":0.9660000205039978,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T14474","display_name":"Industrial Technology and Control Systems","score":0.9204000234603882,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6733502745628357},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.666752815246582},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6288393139839172},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5450979471206665},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.49749329686164856},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47721272706985474},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.45973244309425354},{"id":"https://openalex.org/keywords/recurrent-neural-network","display_name":"Recurrent neural network","score":0.44544848799705505},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.44537052512168884},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43916380405426025},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.4346827566623688},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4254070818424225},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.39874228835105896},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13241007924079895}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6733502745628357},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.666752815246582},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6288393139839172},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5450979471206665},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.49749329686164856},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47721272706985474},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.45973244309425354},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.44544848799705505},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.44537052512168884},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43916380405426025},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.4346827566623688},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4254070818424225},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.39874228835105896},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13241007924079895},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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":1,"locations":[{"id":"doi:10.1109/ijcnn.2008.4633774","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2008.4633774","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.5699999928474426,"display_name":"Reduced inequalities"}],"awards":[],"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":17,"referenced_works":["https://openalex.org/W1516681311","https://openalex.org/W1543439990","https://openalex.org/W1568057090","https://openalex.org/W2077847045","https://openalex.org/W2099227467","https://openalex.org/W2101928083","https://openalex.org/W2115669173","https://openalex.org/W2118204568","https://openalex.org/W2132450099","https://openalex.org/W2147776231","https://openalex.org/W2149974730","https://openalex.org/W2150468523","https://openalex.org/W2156521550","https://openalex.org/W2158810475","https://openalex.org/W2787523326","https://openalex.org/W3101117696","https://openalex.org/W4301791716"],"related_works":["https://openalex.org/W2756132392","https://openalex.org/W2985979428","https://openalex.org/W2510140549","https://openalex.org/W2187449906","https://openalex.org/W4285101096","https://openalex.org/W4382725876","https://openalex.org/W2084892497","https://openalex.org/W2115614142","https://openalex.org/W4320477335","https://openalex.org/W1561889708"],"abstract_inverted_index":{"A":[0],"recurrent":[1],"neural":[2,48,59],"network":[3,49,60],"is":[4,52,72,97],"proposed":[5,58,95],"to":[6,65],"deal":[7],"with":[8,13,37],"the":[9,22,25,47,57,66,75,79,83,90,94],"nonlinear":[10,17],"variational":[11,27],"inequalities":[12],"linear":[14],"equality":[15,23],"and":[16,70],"inequality":[18,28,39],"constraints.":[19,40],"By":[20],"exploiting":[21],"constraints,":[24],"original":[26],"problem":[29,85],"can":[30,61,86],"be":[31,63,87],"transformed":[32],"into":[33],"a":[34],"simplified":[35,45],"one":[36],"only":[38],"Therefore,":[41],"by":[42,99],"solving":[43],"this":[44],"problem,":[46],"architecture":[50],"complexity":[51],"reduced":[53],"dramatically.":[54],"In":[55],"addition,":[56],"also":[62],"applied":[64],"constrained":[67],"optimization":[68,84],"problems,":[69],"it":[71],"proved":[73],"that":[74],"convex":[76],"condition":[77],"on":[78],"objective":[80],"function":[81],"of":[82,93],"relaxed.":[88],"Finally,":[89],"satisfactory":[91],"performance":[92],"approach":[96],"demonstrated":[98],"simulation":[100],"examples.":[101]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
