{"id":"https://openalex.org/W4390422047","doi":"https://doi.org/10.1109/tnnls.2023.3340730","title":"Analysis and Application of Matrix-Form Neural Networks for Fast Matrix-Variable Convex Optimization","display_name":"Analysis and Application of Matrix-Form Neural Networks for Fast Matrix-Variable Convex Optimization","publication_year":2023,"publication_date":"2023-12-29","ids":{"openalex":"https://openalex.org/W4390422047","doi":"https://doi.org/10.1109/tnnls.2023.3340730","pmid":"https://pubmed.ncbi.nlm.nih.gov/38157471"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2023.3340730","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2023.3340730","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5113682730","display_name":"Youshen Xia","orcid":null},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Youshen Xia","raw_affiliation_strings":["College of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"College of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086210154","display_name":"Tiantian Ye","orcid":"https://orcid.org/0000-0002-3309-0044"},"institutions":[{"id":"https://openalex.org/I46520130","display_name":"Chaohu University","ror":"https://ror.org/00mwds915","country_code":"CN","type":"education","lineage":["https://openalex.org/I46520130"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tiantian Ye","raw_affiliation_strings":["Department of Mathematics and Big Data, Chaohu University, Hefei, Anhui, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Big Data, Chaohu University, Hefei, Anhui, China","institution_ids":["https://openalex.org/I46520130"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101522233","display_name":"Liqing Huang","orcid":"https://orcid.org/0000-0003-2420-3921"},"institutions":[{"id":"https://openalex.org/I111753288","display_name":"Fujian Normal University","ror":"https://ror.org/020azk594","country_code":"CN","type":"education","lineage":["https://openalex.org/I111753288"]},{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liqing Huang","raw_affiliation_strings":["College of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing, China","College of Computer and Cyber Security, Fujian Normal University, Fuzhou, China"],"affiliations":[{"raw_affiliation_string":"College of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I200845125"]},{"raw_affiliation_string":"College of Computer and Cyber Security, Fujian Normal University, Fuzhou, China","institution_ids":["https://openalex.org/I111753288"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5113682730"],"corresponding_institution_ids":["https://openalex.org/I200845125"],"apc_list":null,"apc_paid":null,"fwci":2.3337,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.88230267,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"36","issue":"2","first_page":"2259","last_page":"2273"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9983999729156494,"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/T11105","display_name":"Advanced Image Processing Techniques","score":0.9975000023841858,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/recurrent-neural-network","display_name":"Recurrent neural network","score":0.8356568813323975},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6496410965919495},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5425208210945129},{"id":"https://openalex.org/keywords/state-transition-matrix","display_name":"State-transition matrix","score":0.5163837671279907},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5158221125602722},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.49825000762939453},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4947795271873474},{"id":"https://openalex.org/keywords/continuous-optimization","display_name":"Continuous optimization","score":0.480175644159317},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4545017182826996},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44114983081817627},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4105573296546936},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3536093533039093},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.3089546859264374},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.2651376724243164},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.23264506459236145},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.18595772981643677},{"id":"https://openalex.org/keywords/multi-swarm-optimization","display_name":"Multi-swarm optimization","score":0.08548301458358765}],"concepts":[{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.8356568813323975},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6496410965919495},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5425208210945129},{"id":"https://openalex.org/C22629506","wikidata":"https://www.wikidata.org/wiki/Q7602993","display_name":"State-transition matrix","level":4,"score":0.5163837671279907},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5158221125602722},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.49825000762939453},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4947795271873474},{"id":"https://openalex.org/C92995354","wikidata":"https://www.wikidata.org/wiki/Q5165499","display_name":"Continuous optimization","level":4,"score":0.480175644159317},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4545017182826996},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44114983081817627},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4105573296546936},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3536093533039093},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3089546859264374},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.2651376724243164},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.23264506459236145},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18595772981643677},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.08548301458358765},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"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/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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2023.3340730","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2023.3340730","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:38157471","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/38157471","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.4099999964237213,"display_name":"Life in Land"}],"awards":[{"id":"https://openalex.org/G1421636618","display_name":null,"funder_award_id":"62276140","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5860993058","display_name":null,"funder_award_id":"2022J01190","funder_id":"https://openalex.org/F4320321878","funder_display_name":"Natural Science Foundation of Fujian Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321878","display_name":"Natural Science Foundation of Fujian Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W285212305","https://openalex.org/W1516681311","https://openalex.org/W1638789865","https://openalex.org/W1993831841","https://openalex.org/W2011474549","https://openalex.org/W2016315140","https://openalex.org/W2016318937","https://openalex.org/W2030148064","https://openalex.org/W2040236138","https://openalex.org/W2069363802","https://openalex.org/W2102227134","https://openalex.org/W2111986387","https://openalex.org/W2151375450","https://openalex.org/W2155395335","https://openalex.org/W2169555996","https://openalex.org/W2171019910","https://openalex.org/W2187446163","https://openalex.org/W2242049308","https://openalex.org/W2472968238","https://openalex.org/W2526569657","https://openalex.org/W2611328865","https://openalex.org/W2759428153","https://openalex.org/W2805747803","https://openalex.org/W2943413045","https://openalex.org/W2962739357","https://openalex.org/W2963331760","https://openalex.org/W2964736125","https://openalex.org/W2965591199","https://openalex.org/W2968881461","https://openalex.org/W3038509990","https://openalex.org/W3082536235","https://openalex.org/W3122030971","https://openalex.org/W3153934864","https://openalex.org/W3180679528","https://openalex.org/W3207553802","https://openalex.org/W3211588585","https://openalex.org/W4206120861","https://openalex.org/W4226303014","https://openalex.org/W4234534407","https://openalex.org/W4250589301","https://openalex.org/W4281264301","https://openalex.org/W4286424202","https://openalex.org/W4290044043","https://openalex.org/W4299512035"],"related_works":["https://openalex.org/W2353523849","https://openalex.org/W4309490307","https://openalex.org/W4375949242","https://openalex.org/W2957709178","https://openalex.org/W2907206257","https://openalex.org/W308707143","https://openalex.org/W2557644665","https://openalex.org/W2756132392","https://openalex.org/W2792234022","https://openalex.org/W2896890876"],"abstract_inverted_index":{"Matrix-variable":[0],"optimization":[1,7,43],"is":[2,131],"a":[3],"generalization":[4],"of":[5,64,143],"vector-variable":[6],"and":[8,21,36,56,97,137],"has":[9],"been":[10],"found":[11],"to":[12,111,115,133],"have":[13,53],"many":[14],"important":[15],"applications.":[16],"To":[17],"reduce":[18],"computation":[19,144],"time":[20],"storage":[22,95],"requirement,":[23],"this":[24],"article":[25],"presents":[26],"two":[27,49,105],"matrix-form":[28,51,71,83,107,128,138],"recurrent":[29],"neural":[30],"networks":[31],"(RNNs),":[32],"one":[33],"continuous-time":[34,70,77],"model":[35],"another":[37],"discrete-time":[38,82],"model,":[39],"for":[40,59],"solving":[41],"matrix-variable":[42],"problems":[44],"with":[45],"linear":[46],"constraints.":[47],"The":[48,68,80],"proposed":[50,69,81,106,127],"RNNs":[52,108],"low":[54],"complexity":[55],"are":[57,100,109],"suitable":[58],"parallel":[60],"implementation":[61],"in":[62,89,141],"terms":[63,142],"matrix":[65],"state":[66],"space.":[67],"RNN":[72,84,136],"can":[73,85],"significantly":[74],"generalize":[75],"existing":[76],"vector-form":[78,135],"RNN.":[79],"be":[86,112],"effectively":[87],"used":[88],"blind":[90],"image":[91],"restoration,":[92],"where":[93],"the":[94,104,116,126],"requirement":[96],"computational":[98],"cost":[99],"largely":[101],"reduced.":[102],"Theoretically,":[103],"guaranteed":[110],"globally":[113],"convergent":[114],"optimal":[117],"solution":[118],"under":[119],"mild":[120],"conditions.":[121],"Computed":[122],"results":[123],"show":[124],"that":[125],"RNN-based":[129,139],"algorithm":[130],"superior":[132],"related":[134],"algorithms,":[140],"time.":[145]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
