{"id":"https://openalex.org/W2078819283","doi":"https://doi.org/10.1137/060675319","title":"A Hybrid Extragradient-Viscosity Method for Monotone Operators and Fixed Point Problems","display_name":"A Hybrid Extragradient-Viscosity Method for Monotone Operators and Fixed Point Problems","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2078819283","doi":"https://doi.org/10.1137/060675319","mag":"2078819283"},"language":"en","primary_location":{"id":"doi:10.1137/060675319","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060675319","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and 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/A5091006322","display_name":"Paul-\u00c9mile Maing\u00e9","orcid":"https://orcid.org/0000-0001-8146-1375"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Paul-Emile Maing\u00e9","raw_affiliation_strings":["Paul-Emile.Mainge@martinique.univ-ag.fr#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Paul-Emile.Mainge@martinique.univ-ag.fr#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5091006322"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7246,"has_fulltext":false,"cited_by_count":324,"citation_normalized_percentile":{"value":0.92860032,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"47","issue":"3","first_page":"1499","last_page":"1515"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998999834060669,"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":0.9998999834060669,"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":0.994700014591217,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9914000034332275,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/variational-inequality","display_name":"Variational inequality","score":0.8721920251846313},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8652303218841553},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.781265139579773},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.7608771324157715},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.7348368763923645},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.7316431999206543},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6665198802947998},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6254932880401611},{"id":"https://openalex.org/keywords/strongly-monotone","display_name":"Strongly monotone","score":0.6118345856666565},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5291892290115356},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4593499004840851},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.43255889415740967},{"id":"https://openalex.org/keywords/method-of-steepest-descent","display_name":"Method of steepest descent","score":0.4315095543861389},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.42003822326660156},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.41882389783859253},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3216457962989807},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30210328102111816},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07745882868766785}],"concepts":[{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.8721920251846313},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8652303218841553},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.781265139579773},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.7608771324157715},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.7348368763923645},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.7316431999206543},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6665198802947998},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6254932880401611},{"id":"https://openalex.org/C12715386","wikidata":"https://www.wikidata.org/wiki/Q7624691","display_name":"Strongly monotone","level":3,"score":0.6118345856666565},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5291892290115356},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4593499004840851},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.43255889415740967},{"id":"https://openalex.org/C158847443","wikidata":"https://www.wikidata.org/wiki/Q1997812","display_name":"Method of steepest descent","level":2,"score":0.4315095543861389},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.42003822326660156},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.41882389783859253},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3216457962989807},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30210328102111816},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07745882868766785},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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":1,"locations":[{"id":"doi:10.1137/060675319","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060675319","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.550000011920929}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W93786226","https://openalex.org/W1519983908","https://openalex.org/W1685874591","https://openalex.org/W1876574230","https://openalex.org/W1965619116","https://openalex.org/W1974451927","https://openalex.org/W1977111935","https://openalex.org/W1980487211","https://openalex.org/W1987665513","https://openalex.org/W1998554359","https://openalex.org/W2000116885","https://openalex.org/W2005723892","https://openalex.org/W2012193376","https://openalex.org/W2018902042","https://openalex.org/W2042314419","https://openalex.org/W2044040638","https://openalex.org/W2047605837","https://openalex.org/W2049966847","https://openalex.org/W2052611235","https://openalex.org/W2058532290","https://openalex.org/W2059947291","https://openalex.org/W2061750102","https://openalex.org/W2062059813","https://openalex.org/W2065495103","https://openalex.org/W2067100748","https://openalex.org/W2069435104","https://openalex.org/W2070694134","https://openalex.org/W2075106545","https://openalex.org/W2102789047","https://openalex.org/W2132347401","https://openalex.org/W2132614631","https://openalex.org/W2132677982","https://openalex.org/W2138146018","https://openalex.org/W2147161158","https://openalex.org/W2150195104","https://openalex.org/W2162230069","https://openalex.org/W2394608080"],"related_works":["https://openalex.org/W4221091651","https://openalex.org/W1968854694","https://openalex.org/W2037152550","https://openalex.org/W2379024323","https://openalex.org/W1992322822","https://openalex.org/W2094957806","https://openalex.org/W2124505441","https://openalex.org/W4237308164","https://openalex.org/W2999024130","https://openalex.org/W2029398639"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3],"an":[4],"iterative":[5],"method,":[6],"in":[7],"a":[8,14,24,38,43,55,58],"real":[9],"Hilbert":[10],"space,":[11],"for":[12,42],"approximating":[13],"common":[15],"element":[16],"of":[17,20,23,35,37,57,60,79,82],"the":[18,33,61,67,76,80,86],"set":[19,34],"fixed":[21],"points":[22],"demicontractive":[25],"operator":[26],"(possibly":[27],"quasi-nonexpansive":[28],"or":[29],"strictly":[30],"pseudocontractive)":[31],"and":[32,66],"solutions":[36],"variational":[39],"inequality":[40],"problem":[41],"monotone,":[44],"Lipschitz":[45],"continuous":[46],"mapping.":[47],"The":[48],"considered":[49,87],"algorithm":[50],"can":[51],"be":[52],"regarded":[53],"as":[54],"combination":[56],"variation":[59],"hybrid":[62],"steepest":[63],"descent":[64],"method":[65],"so-called":[68],"extragradient":[69],"method.":[70],"Under":[71],"classical":[72],"conditions,":[73],"we":[74],"prove":[75],"strong":[77],"convergence":[78],"sequences":[81],"iterates":[83],"given":[84],"by":[85],"scheme.":[88]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":36},{"year":2024,"cited_by_count":26},{"year":2023,"cited_by_count":34},{"year":2022,"cited_by_count":36},{"year":2021,"cited_by_count":35},{"year":2020,"cited_by_count":38},{"year":2019,"cited_by_count":38},{"year":2018,"cited_by_count":24},{"year":2017,"cited_by_count":14},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":4}],"updated_date":"2026-05-09T13:55:54.758798","created_date":"2025-10-10T00:00:00"}
