{"id":"https://openalex.org/W3048066766","doi":"https://doi.org/10.1109/tnnls.2020.3008661","title":"A Neural Network Based on the Metric Projector for Solving SOCCVI Problem","display_name":"A Neural Network Based on the Metric Projector for Solving SOCCVI Problem","publication_year":2020,"publication_date":"2020-08-05","ids":{"openalex":"https://openalex.org/W3048066766","doi":"https://doi.org/10.1109/tnnls.2020.3008661","mag":"3048066766","pmid":"https://pubmed.ncbi.nlm.nih.gov/32755866"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2020.3008661","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2020.3008661","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/A5102926847","display_name":"Juhe Sun","orcid":"https://orcid.org/0000-0002-1000-1766"},"institutions":[{"id":"https://openalex.org/I125904092","display_name":"Shenyang Aerospace University","ror":"https://ror.org/02423gm04","country_code":"CN","type":"education","lineage":["https://openalex.org/I125904092"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Juhe Sun","raw_affiliation_strings":["School of Science, Shenyang Aerospace University, Shenyang, China"],"raw_orcid":"https://orcid.org/0000-0002-1000-1766","affiliations":[{"raw_affiliation_string":"School of Science, Shenyang Aerospace University, Shenyang, China","institution_ids":["https://openalex.org/I125904092"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012047724","display_name":"Weichen Fu","orcid":"https://orcid.org/0000-0001-9092-7165"},"institutions":[{"id":"https://openalex.org/I125904092","display_name":"Shenyang Aerospace University","ror":"https://ror.org/02423gm04","country_code":"CN","type":"education","lineage":["https://openalex.org/I125904092"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weichen Fu","raw_affiliation_strings":["School of Science, Shenyang Aerospace University, Shenyang, China"],"raw_orcid":"https://orcid.org/0000-0001-9092-7165","affiliations":[{"raw_affiliation_string":"School of Science, Shenyang Aerospace University, Shenyang, China","institution_ids":["https://openalex.org/I125904092"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070538452","display_name":"Jan Harold Alcantara","orcid":"https://orcid.org/0000-0002-7242-4414"},"institutions":[{"id":"https://openalex.org/I134161618","display_name":"National Taiwan Normal University","ror":"https://ror.org/059dkdx38","country_code":"TW","type":"education","lineage":["https://openalex.org/I134161618"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Jan Harold Alcantara","raw_affiliation_strings":["National Taiwan Normal University, Taipei, Taiwan"],"raw_orcid":"https://orcid.org/0000-0002-7242-4414","affiliations":[{"raw_affiliation_string":"National Taiwan Normal University, Taipei, Taiwan","institution_ids":["https://openalex.org/I134161618"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061633817","display_name":"Jein-Shan Chen","orcid":"https://orcid.org/0000-0002-4596-9419"},"institutions":[{"id":"https://openalex.org/I134161618","display_name":"National Taiwan Normal University","ror":"https://ror.org/059dkdx38","country_code":"TW","type":"education","lineage":["https://openalex.org/I134161618"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Jein-Shan Chen","raw_affiliation_strings":["National Taiwan Normal University, Taipei, Taiwan"],"raw_orcid":"https://orcid.org/0000-0002-4596-9419","affiliations":[{"raw_affiliation_string":"National Taiwan Normal University, Taipei, Taiwan","institution_ids":["https://openalex.org/I134161618"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1917,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.48657964,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"32","issue":"7","first_page":"2886","last_page":"2900"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10586","display_name":"Robotic Path Planning Algorithms","score":0.972000002861023,"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"}},"topics":[{"id":"https://openalex.org/T10586","display_name":"Robotic Path Planning Algorithms","score":0.972000002861023,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9696000218391418,"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"}},{"id":"https://openalex.org/T10534","display_name":"Structural Health Monitoring Techniques","score":0.9682999849319458,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/projector","display_name":"Projector","score":0.7057485580444336},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6586325764656067},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6228227615356445},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5860273838043213},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4295770525932312},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.3257557451725006},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.10039326548576355},{"id":"https://openalex.org/keywords/operations-management","display_name":"Operations management","score":0.07311296463012695}],"concepts":[{"id":"https://openalex.org/C2776865275","wikidata":"https://www.wikidata.org/wiki/Q311666","display_name":"Projector","level":2,"score":0.7057485580444336},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6586325764656067},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6228227615356445},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5860273838043213},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4295770525932312},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.3257557451725006},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.10039326548576355},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.07311296463012695}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D011340","descriptor_name":"Problem Solving","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D011340","descriptor_name":"Problem Solving","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D011340","descriptor_name":"Problem Solving","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2020.3008661","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2020.3008661","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:32755866","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/32755866","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/10","score":0.47999998927116394,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G658827598","display_name":null,"funder_award_id":"11301348","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"},{"id":"https://openalex.org/F4320322795","display_name":"Ministry of Science and Technology, Taiwan","ror":"https://ror.org/02kv4zf79"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W1543439990","https://openalex.org/W1551386895","https://openalex.org/W1597286183","https://openalex.org/W1601741115","https://openalex.org/W1965289538","https://openalex.org/W1965717960","https://openalex.org/W1967759264","https://openalex.org/W1972573855","https://openalex.org/W1973281249","https://openalex.org/W1988557613","https://openalex.org/W1990799441","https://openalex.org/W2009923109","https://openalex.org/W2016187009","https://openalex.org/W2019584702","https://openalex.org/W2021720399","https://openalex.org/W2036170323","https://openalex.org/W2068807208","https://openalex.org/W2083128450","https://openalex.org/W2091968661","https://openalex.org/W2093246563","https://openalex.org/W2097113878","https://openalex.org/W2099016540","https://openalex.org/W2102227134","https://openalex.org/W2105235982","https://openalex.org/W2111697351","https://openalex.org/W2116748247","https://openalex.org/W2118204568","https://openalex.org/W2128523553","https://openalex.org/W2133971328","https://openalex.org/W2135728877","https://openalex.org/W2145356049","https://openalex.org/W2150468523","https://openalex.org/W2150872461","https://openalex.org/W2156521550","https://openalex.org/W2156737647","https://openalex.org/W2163296482","https://openalex.org/W2166234392","https://openalex.org/W2170161701","https://openalex.org/W2346957515","https://openalex.org/W2469729643","https://openalex.org/W2889351970","https://openalex.org/W2912097295","https://openalex.org/W2912906782","https://openalex.org/W3141151088","https://openalex.org/W4249513058","https://openalex.org/W4301791716","https://openalex.org/W6720086430"],"related_works":["https://openalex.org/W2772917594","https://openalex.org/W2036807459","https://openalex.org/W2058170566","https://openalex.org/W2755342338","https://openalex.org/W2166024367","https://openalex.org/W3116076068","https://openalex.org/W2229312674","https://openalex.org/W2951359407","https://openalex.org/W2079911747","https://openalex.org/W1969923398"],"abstract_inverted_index":{"We":[0],"propose":[1],"an":[2],"efficient":[3],"neural":[4,103,118,126],"network":[5,16,104,119],"for":[6,46],"solving":[7,106],"the":[8,20,25,34,47,54,74,77,80,85,99,102,116,129],"second-order":[9,64,86],"cone":[10],"constrained":[11],"variational":[12,26],"inequality":[13,27],"(SOCCVI).":[14],"The":[15],"is":[17,30,120],"constructed":[18],"using":[19,42],"Karush-Kuhn-Tucker":[21],"(KKT)":[22],"conditions":[23,66],"of":[24,39,76,79,101,134,139],"(VI),":[28],"which":[29],"used":[31],"to":[32,51,67,141],"recast":[33],"SOCCVI":[35,107,130,142],"as":[36],"a":[37,43],"system":[38,82],"equations":[40],"by":[41],"smoothing":[44],"function":[45],"metric":[48],"projection":[49],"mapping":[50],"deal":[52],"with":[53],"complementarity":[55],"condition.":[56],"Aside":[57],"from":[58],"standard":[59],"stability":[60,135],"results,":[61],"we":[62,72,93],"explore":[63],"sufficient":[65,87],"obtain":[68],"exponential":[69],"stability.":[70],"Especially,":[71],"prove":[73],"nonsingularity":[75],"Jacobian":[78],"KKT":[81],"based":[83],"on":[84],"condition":[88],"and":[89,136],"constraint":[90],"nondegeneracy.":[91],"Finally,":[92],"present":[94],"some":[95],"numerical":[96,110],"experiments,":[97],"illustrating":[98],"efficiency":[100],"in":[105,114,128,132],"problems.":[108],"Our":[109],"simulations":[111],"reveal":[112],"that,":[113],"general,":[115],"new":[117],"more":[121],"dominant":[122],"than":[123],"all":[124],"other":[125],"networks":[127],"literature":[131],"terms":[133],"convergence":[137],"rates":[138],"trajectories":[140],"solution.":[143]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":7},{"year":2022,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
