{"id":"https://openalex.org/W2057069535","doi":"https://doi.org/10.1137/s105262349935949x","title":"The Proximal Point Algorithm with Genuine Superlinear Convergence for the Monotone Complementarity Problem","display_name":"The Proximal Point Algorithm with Genuine Superlinear Convergence for the Monotone Complementarity Problem","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2057069535","doi":"https://doi.org/10.1137/s105262349935949x","mag":"2057069535"},"language":"en","primary_location":{"id":"doi:10.1137/s105262349935949x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s105262349935949x","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","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/A5109115371","display_name":"Nobuo Yamashita","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nobuo Yamashita","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5058813836","display_name":"Masao Fukushima","orcid":"https://orcid.org/0000-0002-4372-6376"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Masao Fukushima","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5109115371"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8107,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.90465288,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"11","issue":"2","first_page":"364","last_page":"379"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9993000030517578,"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/T13855","display_name":"Aerospace Engineering and Control Systems","score":0.9918000102043152,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/mathematics","display_name":"Mathematics","score":0.8758851289749146},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.7841723561286926},{"id":"https://openalex.org/keywords/complementarity","display_name":"Complementarity (molecular biology)","score":0.7053806781768799},{"id":"https://openalex.org/keywords/complementarity-theory","display_name":"Complementarity theory","score":0.6217064261436462},{"id":"https://openalex.org/keywords/mixed-complementarity-problem","display_name":"Mixed complementarity problem","score":0.5781395435333252},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5624480247497559},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4878418445587158},{"id":"https://openalex.org/keywords/nonlinear-complementarity-problem","display_name":"Nonlinear complementarity problem","score":0.4331017732620239},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4197392463684082},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3610430657863617},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34943562746047974},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08450150489807129}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8758851289749146},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.7841723561286926},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.7053806781768799},{"id":"https://openalex.org/C85404239","wikidata":"https://www.wikidata.org/wiki/Q5156417","display_name":"Complementarity theory","level":3,"score":0.6217064261436462},{"id":"https://openalex.org/C77196050","wikidata":"https://www.wikidata.org/wiki/Q6883962","display_name":"Mixed complementarity problem","level":3,"score":0.5781395435333252},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5624480247497559},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4878418445587158},{"id":"https://openalex.org/C2778646529","wikidata":"https://www.wikidata.org/wiki/Q16948724","display_name":"Nonlinear complementarity problem","level":4,"score":0.4331017732620239},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4197392463684082},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3610430657863617},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34943562746047974},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08450150489807129},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s105262349935949x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s105262349935949x","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.44.3717","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.44.3717","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.kuamp.kyoto-u.ac.jp/labs/optima/member/staff/nobuo/papers/proximal.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.50.2183","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.2183","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://halo.kuamp.kyoto-u.ac.jp/zagato/member/staff/fuku/./papers/genuine.ps.Z","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4000000059604645,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W104144503","https://openalex.org/W1551360398","https://openalex.org/W1969073096","https://openalex.org/W1997671037","https://openalex.org/W2036930530","https://openalex.org/W2038497950","https://openalex.org/W2053643774","https://openalex.org/W2055467852","https://openalex.org/W2090689930","https://openalex.org/W2090694590","https://openalex.org/W2140603012","https://openalex.org/W2160068964","https://openalex.org/W2587712072","https://openalex.org/W2971350920","https://openalex.org/W4248555053","https://openalex.org/W4252641252"],"related_works":["https://openalex.org/W2276648117","https://openalex.org/W2091810828","https://openalex.org/W2085004531","https://openalex.org/W2774961640","https://openalex.org/W2157124849","https://openalex.org/W2128234186","https://openalex.org/W564691918","https://openalex.org/W2022470868","https://openalex.org/W2011175430","https://openalex.org/W4297794397"],"abstract_inverted_index":{"In":[0,64],"this":[1,65],"paper,":[2,66],"we":[3,67,93,119],"consider":[4],"a":[5,19,129],"proximal":[6],"point":[7,136],"algorithm":[8],"(PPA)":[9],"for":[10,45],"solving":[11,22],"monotone":[12],"nonlinear":[13],"complementarity":[14,140],"problems":[15],"(NCP).":[16],"PPA":[17,35,97],"generates":[18],"sequence":[20],"by":[21,74],"subproblems":[23,58,82],"that":[24,34,95,101,121,133],"are":[25],"regularizations":[26],"of":[27,48,105,116,124],"the":[28,69,90,96,102,106,113,117,122,134,138],"original":[29],"problem.":[30],"It":[31],"is":[32,52,108,126],"known":[33],"has":[36],"global":[37],"and":[38,78,83],"superlinear":[39,127],"convergence":[40,125],"properties":[41],"under":[42],"appropriate":[43],"criteria":[44],"approximate":[46],"solutions":[47],"subproblems.":[49],"However,":[50],"it":[51],"not":[53],"always":[54],"easy":[55],"to":[56,60,80,88],"solve":[57,81],"or":[59],"check":[61,89],"those":[62],"criteria.":[63,91],"adopt":[68,84],"generalized":[70],"Newton":[71],"method":[72],"proposed":[73],"De":[75],"Luca,":[76],"Facchinei,":[77],"Kanzow":[79],"some":[85],"NCP":[86],"functions":[87],"Then":[92],"show":[94,120],"converges":[98],"globally":[99],"provided":[100,132],"solution":[103],"set":[104],"problem":[107],"nonempty.":[109],"Moreover,":[110],"without":[111],"assuming":[112],"local":[114],"uniqueness":[115],"solution,":[118],"rate":[123],"in":[128],"genuine":[130],"sense,":[131],"limit":[135],"satisfies":[137],"strict":[139],"condition.":[141]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
