{"id":"https://openalex.org/W2131539613","doi":"https://doi.org/10.1080/10556780500397074","title":"A norm descent BFGS method for solving KKT systems of symmetric variational inequality problems","display_name":"A norm descent BFGS method for solving KKT systems of symmetric variational inequality problems","publication_year":2006,"publication_date":"2006-05-03","ids":{"openalex":"https://openalex.org/W2131539613","doi":"https://doi.org/10.1080/10556780500397074","mag":"2131539613"},"language":"en","primary_location":{"id":"doi:10.1080/10556780500397074","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780500397074","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"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":"Optimization Methods and Software","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/A5100353050","display_name":"Jiwei Zhang","orcid":"https://orcid.org/0000-0002-7454-1673"},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]},{"id":"https://openalex.org/I198357462","display_name":"Changsha University","ror":"https://ror.org/011d8sm39","country_code":"CN","type":"education","lineage":["https://openalex.org/I198357462"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ji-Wei Zhang","raw_affiliation_strings":["\n Institute of Applied Mathematics, Hunan University, Changsha, 410082, China","Institute of Applied Mathematics, Hunan University, Changsha, China#TAB#"],"affiliations":[{"raw_affiliation_string":"\n Institute of Applied Mathematics, Hunan University, Changsha, 410082, China","institution_ids":["https://openalex.org/I198357462","https://openalex.org/I16609230"]},{"raw_affiliation_string":"Institute of Applied Mathematics, Hunan University, Changsha, China#TAB#","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100336705","display_name":"Donghui Li","orcid":"https://orcid.org/0000-0003-3335-4537"},"institutions":[{"id":"https://openalex.org/I198357462","display_name":"Changsha University","ror":"https://ror.org/011d8sm39","country_code":"CN","type":"education","lineage":["https://openalex.org/I198357462"]},{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Dong-Hui Li","raw_affiliation_strings":["\n Institute of Applied Mathematics, Hunan University, Changsha, 410082, China","Institute of Applied Mathematics, Hunan University, Changsha, China#TAB#"],"affiliations":[{"raw_affiliation_string":"\n Institute of Applied Mathematics, Hunan University, Changsha, 410082, China","institution_ids":["https://openalex.org/I198357462","https://openalex.org/I16609230"]},{"raw_affiliation_string":"Institute of Applied Mathematics, Hunan University, Changsha, China#TAB#","institution_ids":["https://openalex.org/I16609230"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100336705"],"corresponding_institution_ids":["https://openalex.org/I16609230","https://openalex.org/I198357462"],"apc_list":null,"apc_paid":null,"fwci":0.9066,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.75568037,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"22","issue":"2","first_page":"237","last_page":"252"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9991000294685364,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9775999784469604,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/karush\u2013kuhn\u2013tucker-conditions","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","score":0.9042395353317261},{"id":"https://openalex.org/keywords/broyden\u2013fletcher\u2013goldfarb\u2013shanno-algorithm","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","score":0.7268849611282349},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.6982886791229248},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6136295795440674},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5602011680603027},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5237022638320923},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.4642959535121918},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.45286083221435547},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38069871068000793},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22697985172271729},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18188294768333435},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.08174639940261841},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.06682717800140381},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.05882951617240906}],"concepts":[{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.9042395353317261},{"id":"https://openalex.org/C132721684","wikidata":"https://www.wikidata.org/wiki/Q2877013","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","level":3,"score":0.7268849611282349},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.6982886791229248},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6136295795440674},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5602011680603027},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5237022638320923},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.4642959535121918},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.45286083221435547},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38069871068000793},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22697985172271729},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18188294768333435},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.08174639940261841},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.06682717800140381},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.05882951617240906},{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556780500397074","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780500397074","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"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":"Optimization Methods and Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.6100000143051147}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W11974643","https://openalex.org/W97365357","https://openalex.org/W1563731874","https://openalex.org/W1968932160","https://openalex.org/W1991271057","https://openalex.org/W1992688650","https://openalex.org/W2067547116","https://openalex.org/W2070890393","https://openalex.org/W2151902790","https://openalex.org/W2153532571","https://openalex.org/W2171998255"],"related_works":["https://openalex.org/W2155858901","https://openalex.org/W2491194410","https://openalex.org/W4382519099","https://openalex.org/W1515727993","https://openalex.org/W2037179686","https://openalex.org/W2802398440","https://openalex.org/W97365357","https://openalex.org/W3161161632","https://openalex.org/W2368227208","https://openalex.org/W2805121365"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,22,63],"article,":[3],"the":[4,8,19,54,73],"KKT":[5],"system":[6],"of":[7,21,62,78],"variational":[9,40],"inequality":[10,41],"problem":[11],"is":[12,29,33],"reformulated":[13],"as":[14],"a":[15,24],"nonsmooth":[16],"equation.":[17],"On":[18],"basis":[20],"reformulation,":[23],"norm":[25],"descent":[26],"BFGS":[27],"method":[28,32],"proposed.":[30],"The":[31,48],"globally":[34],"and":[35,65],"superlinearly":[36],"convergent.":[37],"Keywords:":[38],"Symmetric":[39],"problemKKT":[42],"systemBFGS":[43],"methodGlobal":[44],"convergenceSuperlinear":[45],"convergence":[46],"Acknowledgements":[47],"authors":[49],"would":[50],"like":[51],"to":[52],"thank":[53],"two":[55],"anonymous":[56],"referees":[57],"for":[58],"their":[59],"careful":[60],"reading":[61],"article":[64],"valuable":[66],"comments.":[67],"This":[68],"work":[69],"was":[70],"supported":[71],"by":[72],"National":[74],"Natural":[75],"Science":[76],"Foundation":[77],"China":[79],"via":[80],"grant":[81],"10471036.":[82]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
