{"id":"https://openalex.org/W2560101520","doi":"https://doi.org/10.3390/a9040083","title":"Nonsmooth Levenberg-Marquardt Type Method for Solving a Class of Stochastic Linear Complementarity Problems with Finitely Many Elements","display_name":"Nonsmooth Levenberg-Marquardt Type Method for Solving a Class of Stochastic Linear Complementarity Problems with Finitely Many Elements","publication_year":2016,"publication_date":"2016-12-06","ids":{"openalex":"https://openalex.org/W2560101520","doi":"https://doi.org/10.3390/a9040083","mag":"2560101520"},"language":"en","primary_location":{"id":"doi:10.3390/a9040083","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a9040083","pdf_url":"https://www.mdpi.com/1999-4893/9/4/83/pdf?version=1481011847","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"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":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/9/4/83/pdf?version=1481011847","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100739134","display_name":"Zhimin Liu","orcid":"https://orcid.org/0009-0004-8303-8684"},"institutions":[{"id":"https://openalex.org/I108688024","display_name":"Qingdao University","ror":"https://ror.org/021cj6z65","country_code":"CN","type":"education","lineage":["https://openalex.org/I108688024"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhimin Liu","raw_affiliation_strings":["School of Mathematics and Statistics, Qingdao University, 308 Qingdao Ningxia Road, Qingdao 266071, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Qingdao University, 308 Qingdao Ningxia Road, Qingdao 266071, China","institution_ids":["https://openalex.org/I108688024"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102939973","display_name":"Shou-qiang Du","orcid":"https://orcid.org/0000-0002-3854-3479"},"institutions":[{"id":"https://openalex.org/I108688024","display_name":"Qingdao University","ror":"https://ror.org/021cj6z65","country_code":"CN","type":"education","lineage":["https://openalex.org/I108688024"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shouqiang Du","raw_affiliation_strings":["School of Mathematics and Statistics, Qingdao University, 308 Qingdao Ningxia Road, Qingdao 266071, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Qingdao University, 308 Qingdao Ningxia Road, Qingdao 266071, China","institution_ids":["https://openalex.org/I108688024"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101710061","display_name":"Ruiying Wang","orcid":"https://orcid.org/0000-0001-7823-266X"},"institutions":[{"id":"https://openalex.org/I108688024","display_name":"Qingdao University","ror":"https://ror.org/021cj6z65","country_code":"CN","type":"education","lineage":["https://openalex.org/I108688024"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ruiying Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Qingdao University, 308 Qingdao Ningxia Road, Qingdao 266071, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Qingdao University, 308 Qingdao Ningxia Road, Qingdao 266071, China","institution_ids":["https://openalex.org/I108688024"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102939973"],"corresponding_institution_ids":["https://openalex.org/I108688024"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.4563,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.67430237,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"9","issue":"4","first_page":"83","last_page":"83"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9926000237464905,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.9789999723434448,"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/levenberg\u2013marquardt-algorithm","display_name":"Levenberg\u2013Marquardt algorithm","score":0.7665526866912842},{"id":"https://openalex.org/keywords/complementarity","display_name":"Complementarity (molecular biology)","score":0.7451862096786499},{"id":"https://openalex.org/keywords/mixed-complementarity-problem","display_name":"Mixed complementarity problem","score":0.7287633419036865},{"id":"https://openalex.org/keywords/linear-complementarity-problem","display_name":"Linear complementarity problem","score":0.6852887868881226},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6197396516799927},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6171882152557373},{"id":"https://openalex.org/keywords/complementarity-theory","display_name":"Complementarity theory","score":0.5572682023048401},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.416047602891922},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41069167852401733},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3067389726638794},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.17341011762619019},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.15112003684043884},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08406677842140198}],"concepts":[{"id":"https://openalex.org/C87578567","wikidata":"https://www.wikidata.org/wiki/Q1426494","display_name":"Levenberg\u2013Marquardt algorithm","level":3,"score":0.7665526866912842},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.7451862096786499},{"id":"https://openalex.org/C77196050","wikidata":"https://www.wikidata.org/wiki/Q6883962","display_name":"Mixed complementarity problem","level":3,"score":0.7287633419036865},{"id":"https://openalex.org/C34320192","wikidata":"https://www.wikidata.org/wiki/Q783105","display_name":"Linear complementarity problem","level":3,"score":0.6852887868881226},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6197396516799927},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6171882152557373},{"id":"https://openalex.org/C85404239","wikidata":"https://www.wikidata.org/wiki/Q5156417","display_name":"Complementarity theory","level":3,"score":0.5572682023048401},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.416047602891922},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41069167852401733},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3067389726638794},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.17341011762619019},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.15112003684043884},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08406677842140198},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/a9040083","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a9040083","pdf_url":"https://www.mdpi.com/1999-4893/9/4/83/pdf?version=1481011847","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"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":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:f4a159fa064f479e9f7d71ae6e2bc180","is_oa":true,"landing_page_url":"https://doaj.org/article/f4a159fa064f479e9f7d71ae6e2bc180","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 9, Iss 4, p 83 (2016)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/a9040083","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a9040083","pdf_url":"https://www.mdpi.com/1999-4893/9/4/83/pdf?version=1481011847","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"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":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2560101520.pdf","grobid_xml":"https://content.openalex.org/works/W2560101520.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W68594018","https://openalex.org/W1543439990","https://openalex.org/W1965289538","https://openalex.org/W1973323102","https://openalex.org/W1979460428","https://openalex.org/W1979801491","https://openalex.org/W1982172737","https://openalex.org/W1992688650","https://openalex.org/W2006464899","https://openalex.org/W2008598111","https://openalex.org/W2030169236","https://openalex.org/W2030824567","https://openalex.org/W2051269616","https://openalex.org/W2054831316","https://openalex.org/W2057613951","https://openalex.org/W2068042327","https://openalex.org/W2078816386","https://openalex.org/W2087136707","https://openalex.org/W2119279696","https://openalex.org/W2123093332","https://openalex.org/W2126194142","https://openalex.org/W2135728877","https://openalex.org/W2147977073","https://openalex.org/W2149255010","https://openalex.org/W2161608164","https://openalex.org/W2164249077","https://openalex.org/W3106992008","https://openalex.org/W3141010354","https://openalex.org/W6651854764"],"related_works":["https://openalex.org/W2276648117","https://openalex.org/W2063320018","https://openalex.org/W2042813889","https://openalex.org/W2358901572","https://openalex.org/W2028943836","https://openalex.org/W4220847489","https://openalex.org/W2091810828","https://openalex.org/W819098253","https://openalex.org/W1548220668","https://openalex.org/W2765841216"],"abstract_inverted_index":{"Our":[0],"purpose":[1],"of":[2,10,35,61],"this":[3],"paper":[4],"is":[5,41,79],"to":[6],"solve":[7],"a":[8,22,29,52],"class":[9],"stochastic":[11,24,37,90],"linear":[12,25,38,91],"complementarity":[13,26,39,92],"problems":[14],"(SLCP)":[15],"with":[16],"finitely":[17],"many":[18],"elements.":[19],"Based":[20],"on":[21],"new":[23,30],"problem":[27,40,86],"function,":[28],"semi-smooth":[31,46],"least":[32,47],"squares":[33,48],"reformulation":[34],"the":[36,45,62,70,76,82,88],"introduced.":[42],"For":[43],"solving":[44],"reformulation,":[49],"we":[50],"propose":[51],"feasible":[53],"nonsmooth":[54,63],"Levenberg\u2013Marquardt-type":[55,64],"method.":[56],"The":[57],"global":[58],"convergence":[59],"properties":[60],"method":[65,78],"are":[66],"also":[67],"presented.":[68],"Finally,":[69],"related":[71,83],"numerical":[72],"results":[73],"illustrate":[74],"that":[75],"proposed":[77],"efficient":[80],"for":[81],"refinery":[84],"production":[85],"and":[87],"large-scale":[89],"problems.":[93]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}