{"id":"https://openalex.org/W2047839295","doi":"https://doi.org/10.1007/s10589-010-9372-0","title":"Proximal-like contraction methods for monotone variational inequalities in a unified framework I: Effective quadruplet and primary methods","display_name":"Proximal-like contraction methods for monotone variational inequalities in a unified framework I: Effective quadruplet and primary methods","publication_year":2010,"publication_date":"2010-11-17","ids":{"openalex":"https://openalex.org/W2047839295","doi":"https://doi.org/10.1007/s10589-010-9372-0","mag":"2047839295"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-010-9372-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-010-9372-0","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","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/A5039946576","display_name":"Bingsheng He","orcid":"https://orcid.org/0000-0001-8618-4581"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bingsheng He","raw_affiliation_strings":["Department of Mathematics, Nanjing University, Nanjing, 210093, China","National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Nanjing University, Nanjing, 210093, China","institution_ids":["https://openalex.org/I881766915"]},{"raw_affiliation_string":"National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079973146","display_name":"Li\u2010Zhi Liao","orcid":"https://orcid.org/0000-0002-0588-7953"},"institutions":[{"id":"https://openalex.org/I141568987","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131","country_code":"HK","type":"education","lineage":["https://openalex.org/I141568987"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Li-Zhi Liao","raw_affiliation_strings":["Department of Mathematics, Hong Kong Baptist University, Hong Kong, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hong Kong Baptist University, Hong Kong, China","institution_ids":["https://openalex.org/I141568987"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100389014","display_name":"Xiang Wang","orcid":"https://orcid.org/0000-0002-2135-8576"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiang Wang","raw_affiliation_strings":["Department of Mathematics, Nanjing University, Nanjing, 210093, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Nanjing University, Nanjing, 210093, China","institution_ids":["https://openalex.org/I881766915"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5039946576"],"corresponding_institution_ids":["https://openalex.org/I881766915"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.0251,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.77207324,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"51","issue":"2","first_page":"649","last_page":"679"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9994000196456909,"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":0.9994000196456909,"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":0.996999979019165,"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":0.9879999756813049,"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/mathematics","display_name":"Mathematics","score":0.8497796654701233},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6796479225158691},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.637619137763977},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5953450798988342},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4871980547904968},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4798707067966461},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.47904646396636963},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4308116137981415},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40315672755241394},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34376242756843567},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23836523294448853},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14590778946876526}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8497796654701233},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6796479225158691},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.637619137763977},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5953450798988342},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4871980547904968},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4798707067966461},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.47904646396636963},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4308116137981415},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40315672755241394},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34376242756843567},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23836523294448853},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14590778946876526},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","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/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"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":3,"locations":[{"id":"doi:10.1007/s10589-010-9372-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-010-9372-0","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:coopap:v:51:y:2012:i:2:p:649-679","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s10589-010-9372-0","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:repository.hkbu.edu.hk:hkbu_staff_publication-2098","is_oa":false,"landing_page_url":"https://repository.hkbu.edu.hk/hkbu_staff_publication/1084","pdf_url":null,"source":{"id":"https://openalex.org/S4377196872","display_name":"HKBU Institutional Repository (Hong Kong Baptist University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I141568987","host_organization_name":"Hong Kong Baptist University","host_organization_lineage":["https://openalex.org/I141568987"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"HKBU Staff Publication","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4399999976158142}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W257907672","https://openalex.org/W965503749","https://openalex.org/W1488903562","https://openalex.org/W1519983590","https://openalex.org/W1543439990","https://openalex.org/W1603765807","https://openalex.org/W1967077838","https://openalex.org/W1979735396","https://openalex.org/W1982011875","https://openalex.org/W2026517977","https://openalex.org/W2033736734","https://openalex.org/W2038497950","https://openalex.org/W2039771911","https://openalex.org/W2055467852","https://openalex.org/W2058164831","https://openalex.org/W2069356606","https://openalex.org/W2112980792","https://openalex.org/W2124125796","https://openalex.org/W2135779729","https://openalex.org/W2985272081","https://openalex.org/W3199149775","https://openalex.org/W4242859866","https://openalex.org/W4301283118"],"related_works":["https://openalex.org/W2277178691","https://openalex.org/W4364383069","https://openalex.org/W1965216220","https://openalex.org/W2350630885","https://openalex.org/W3191967975","https://openalex.org/W3142454382","https://openalex.org/W2332288878","https://openalex.org/W3109616988","https://openalex.org/W4287588948","https://openalex.org/W2371658159"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}