{"id":"https://openalex.org/W2073390894","doi":"https://doi.org/10.1155/2012/503242","title":"A Proximal Analytic Center Cutting Plane Algorithm for Solving Variational Inequality Problems","display_name":"A Proximal Analytic Center Cutting Plane Algorithm for Solving Variational Inequality Problems","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2073390894","doi":"https://doi.org/10.1155/2012/503242","mag":"2073390894"},"language":"en","primary_location":{"id":"doi:10.1155/2012/503242","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/503242","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/503242.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2012/503242.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044333609","display_name":"Jie Shen","orcid":"https://orcid.org/0000-0001-6157-3388"},"institutions":[{"id":"https://openalex.org/I153374732","display_name":"Liaoning Normal University","ror":"https://ror.org/04c3cgg32","country_code":"CN","type":"education","lineage":["https://openalex.org/I153374732"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jie Shen","raw_affiliation_strings":["School of Mathematics, Liaoning Normal University, Dalian 116029"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Liaoning Normal University, Dalian 116029","institution_ids":["https://openalex.org/I153374732"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044662952","display_name":"Li-Ping Pang","orcid":"https://orcid.org/0000-0003-2046-3582"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li-Ping Pang","raw_affiliation_strings":["School of Mathematical Sciences, Dalian University of Technology, Dalian 116024"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Dalian University of Technology, Dalian 116024","institution_ids":["https://openalex.org/I27357992"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5044333609"],"corresponding_institution_ids":["https://openalex.org/I153374732"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.6944,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.72414863,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"2012","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9986000061035156,"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":0.9986000061035156,"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":0.9986000061035156,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/convergence","display_name":"Convergence (economics)","score":0.7575191259384155},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.6811464428901672},{"id":"https://openalex.org/keywords/cutting-plane-method","display_name":"Cutting-plane method","score":0.6558908820152283},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6486174464225769},{"id":"https://openalex.org/keywords/center","display_name":"Center (category theory)","score":0.6095954179763794},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.557757556438446},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4773150384426117},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39110225439071655},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37732556462287903},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.26418817043304443},{"id":"https://openalex.org/keywords/crystallography","display_name":"Crystallography","score":0.04263877868652344}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7575191259384155},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.6811464428901672},{"id":"https://openalex.org/C109839438","wikidata":"https://www.wikidata.org/wiki/Q1762039","display_name":"Cutting-plane method","level":3,"score":0.6558908820152283},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6486174464225769},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.6095954179763794},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.557757556438446},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4773150384426117},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39110225439071655},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37732556462287903},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.26418817043304443},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.04263877868652344},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2012/503242","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/503242","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/503242.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1374003986","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1374003986","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:503242","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2012/503242.xml","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:doaj.org/article:583cae52e1144f1e9651957c21e7c4aa","is_oa":true,"landing_page_url":"https://doaj.org/article/583cae52e1144f1e9651957c21e7c4aa","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2012 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2012/503242","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/503242","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/503242.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6499999761581421,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G6267493176","display_name":null,"funder_award_id":"L2010235","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6482682143","display_name":"\u51e0\u7c7b\u91cd\u8981\u7684\u975e\u5149\u6ed1\u4f18\u5316\u95ee\u9898\u7684\u6709\u6548\u7b97\u6cd5\u7684\u7814\u7a76","funder_award_id":"11171138","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6511482496","display_name":null,"funder_award_id":"11171049","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2073390894.pdf","grobid_xml":"https://content.openalex.org/works/W2073390894.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W65890461","https://openalex.org/W76540705","https://openalex.org/W132639066","https://openalex.org/W1501019507","https://openalex.org/W1503492992","https://openalex.org/W1574923065","https://openalex.org/W1636353766","https://openalex.org/W1966986674","https://openalex.org/W1972504036","https://openalex.org/W1992896291","https://openalex.org/W2015681706","https://openalex.org/W2089472568","https://openalex.org/W2093246563","https://openalex.org/W2095365233","https://openalex.org/W2112436371","https://openalex.org/W2137983211","https://openalex.org/W2149570417","https://openalex.org/W2798766386","https://openalex.org/W2895899761","https://openalex.org/W3146803896","https://openalex.org/W4235178178","https://openalex.org/W4240630660","https://openalex.org/W6754817527"],"related_works":["https://openalex.org/W2362705850","https://openalex.org/W2909053289","https://openalex.org/W829267240","https://openalex.org/W1154119719","https://openalex.org/W2379672298","https://openalex.org/W2104243281","https://openalex.org/W1513565830","https://openalex.org/W3012113686","https://openalex.org/W1996239617","https://openalex.org/W3197304203"],"abstract_inverted_index":{"Under":[0],"the":[1,4,33,39,44,54,61],"condition":[2],"that":[3],"values":[5],"of":[6,32,63],"mapping":[7],"F":[8],"are":[9,47],"evaluated":[10],"approximately,":[11],"we":[12,41],"propose":[13],"a":[14],"proximal":[15],"analytic":[16],"center":[17],"cutting":[18,35],"plane":[19,36],"algorithm":[20,56],"for":[21,53],"solving":[22],"variational":[23],"inequalities.":[24],"It":[25],"can":[26],"be":[27],"considered":[28],"as":[29],"an":[30],"approximation":[31],"earlier":[34],"method,":[37],"and":[38],"conditions":[40],"impose":[42],"on":[43],"corresponding":[45],"mappings":[46],"more":[48],"relaxed.":[49],"The":[50],"convergence":[51],"analysis":[52],"proposed":[55],"is":[57],"also":[58],"given":[59],"at":[60],"end":[62],"this":[64],"paper.":[65]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2025-10-10T00:00:00"}
