{"id":"https://openalex.org/W1990449719","doi":"https://doi.org/10.1080/00207160.2015.1040780","title":"Smoothing projected cyclic Barzilai\u2013Borwein method for stochastic linear complementarity problems","display_name":"Smoothing projected cyclic Barzilai\u2013Borwein method for stochastic linear complementarity problems","publication_year":2015,"publication_date":"2015-04-16","ids":{"openalex":"https://openalex.org/W1990449719","doi":"https://doi.org/10.1080/00207160.2015.1040780","mag":"1990449719"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2015.1040780","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1040780","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-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/A5057587509","display_name":"Yakui Huang","orcid":"https://orcid.org/0000-0001-6149-3222"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yakui Huang","raw_affiliation_strings":["School of Mathematics and Statistics, Xidian University, Xi'an 710126, China","School of Mathematics and Statistics, Xidian University, Xi'an710126, China#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xidian University, Xi'an 710126, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Xidian University, Xi'an710126, China#TAB#","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100411968","display_name":"Hongwei Liu","orcid":"https://orcid.org/0000-0003-4046-163X"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongwei Liu","raw_affiliation_strings":["School of Mathematics and Statistics, Xidian University, Xi'an 710126, China","School of Mathematics and Statistics, Xidian University, Xi'an710126, China#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xidian University, Xi'an 710126, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Xidian University, Xi'an710126, China#TAB#","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067535569","display_name":"Tengteng Yu","orcid":"https://orcid.org/0000-0001-6860-9435"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tengteng Yu","raw_affiliation_strings":["School of Mathematics and Statistics, Xidian University, Xi'an 710126, China","School of Mathematics and Statistics, Xidian University, Xi'an710126, China#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xidian University, Xi'an 710126, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Xidian University, Xi'an710126, China#TAB#","institution_ids":["https://openalex.org/I149594827"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5057587509"],"corresponding_institution_ids":["https://openalex.org/I149594827"],"apc_list":null,"apc_paid":null,"fwci":0.3505,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.63477,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"93","issue":"7","first_page":"1188","last_page":"1199"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9988999962806702,"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":0.9988999962806702,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9987999796867371,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.9908000230789185,"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/smoothing","display_name":"Smoothing","score":0.8238524198532104},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7239379286766052},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.6413543224334717},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.6131100654602051},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5009233951568604},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.49700644612312317},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4778168499469757},{"id":"https://openalex.org/keywords/complementarity","display_name":"Complementarity (molecular biology)","score":0.46847477555274963},{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.412765234708786},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41237926483154297},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.31077510118484497},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1550980806350708},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15476754307746887}],"concepts":[{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.8238524198532104},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7239379286766052},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.6413543224334717},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.6131100654602051},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5009233951568604},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.49700644612312317},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4778168499469757},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.46847477555274963},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.412765234708786},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41237926483154297},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31077510118484497},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1550980806350708},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15476754307746887},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2015.1040780","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1040780","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1486993561","https://openalex.org/W1546266651","https://openalex.org/W1551360398","https://openalex.org/W1972770552","https://openalex.org/W1973734200","https://openalex.org/W1979460428","https://openalex.org/W1983916623","https://openalex.org/W1984395157","https://openalex.org/W2005148680","https://openalex.org/W2007504050","https://openalex.org/W2013230381","https://openalex.org/W2015957593","https://openalex.org/W2030824567","https://openalex.org/W2038308486","https://openalex.org/W2043430160","https://openalex.org/W2062950692","https://openalex.org/W2067098824","https://openalex.org/W2076605490","https://openalex.org/W2078816386","https://openalex.org/W2087616929","https://openalex.org/W2098000549","https://openalex.org/W2098132613","https://openalex.org/W2118075667","https://openalex.org/W2144331407","https://openalex.org/W2147977073","https://openalex.org/W2151902790","https://openalex.org/W2167137033","https://openalex.org/W2774032669","https://openalex.org/W4244633107","https://openalex.org/W4249513058","https://openalex.org/W4301791716"],"related_works":["https://openalex.org/W2521519254","https://openalex.org/W3139833644","https://openalex.org/W3121651473","https://openalex.org/W2383807498","https://openalex.org/W2033758151","https://openalex.org/W3074070670","https://openalex.org/W4372300460","https://openalex.org/W2050193462","https://openalex.org/W2107854223","https://openalex.org/W1969207618"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,78],"propose":[4],"a":[5,54,87],"smoothing":[6,30],"projected":[7,34],"cyclic":[8,40],"Barzilai\u2013Borwein":[9,35],"(SPCBB)":[10],"method":[11,27,85,101],"for":[12,49],"solving":[13],"the":[14,29,33,39,45,63,72,80,83,100],"expected":[15],"residual":[16],"minimization":[17],"formulation":[18],"of":[19,62,82,94],"stochastic":[20],"linear":[21],"complementarity":[22],"problems":[23],"(SLCPs).":[24],"The":[25],"SPCBB":[26],"combines":[28],"techniques":[31],"and":[32,53],"(BB)":[36],"method,":[37],"where":[38],"BB":[41,47],"scheme":[42],"which":[43],"resues":[44],"same":[46],"stepsize":[48],"several":[50],"consecutive":[51],"iterations":[52],"nonmonotone":[55],"line":[56],"search":[57],"that":[58,99],"requires":[59],"an":[60],"average":[61],"successive":[64],"function":[65],"values":[66],"decreases":[67],"are":[68],"employed":[69],"to":[70,86],"accelerate":[71],"convergence":[73,81],"process.":[74],"Under":[75],"mild":[76],"conditions,":[77],"show":[79,98],"proposed":[84],"Clarke":[88],"stationary":[89],"point.":[90],"Preliminary":[91],"numerical":[92],"results":[93],"randomly":[95],"generated":[96],"SLCPs":[97],"is":[102],"promising.":[103]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}