{"id":"https://openalex.org/W1964555243","doi":"https://doi.org/10.1007/s11590-009-0141-x","title":"A method of duality for a mixed vector equilibrium problem","display_name":"A method of duality for a mixed vector equilibrium problem","publication_year":2009,"publication_date":"2009-09-15","ids":{"openalex":"https://openalex.org/W1964555243","doi":"https://doi.org/10.1007/s11590-009-0141-x","mag":"1964555243"},"language":"en","primary_location":{"id":"doi:10.1007/s11590-009-0141-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-009-0141-x","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"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":"Optimization Letters","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/A5007676670","display_name":"S. J. Li","orcid":null},"institutions":[{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"S. J. Li","raw_affiliation_strings":["College of Mathematics and Science, Chongqing University, 400030, Chongqing, China","Chongqing University"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Science, Chongqing University, 400030, Chongqing, China","institution_ids":["https://openalex.org/I158842170"]},{"raw_affiliation_string":"Chongqing University","institution_ids":["https://openalex.org/I158842170"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102809305","display_name":"Pei Zhao","orcid":"https://orcid.org/0000-0002-9647-6585"},"institutions":[{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"P. Zhao","raw_affiliation_strings":["College of Mathematics and Science, Chongqing University, 400030, Chongqing, China","Chongqing University"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Science, Chongqing University, 400030, Chongqing, China","institution_ids":["https://openalex.org/I158842170"]},{"raw_affiliation_string":"Chongqing University","institution_ids":["https://openalex.org/I158842170"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5007676670"],"corresponding_institution_ids":["https://openalex.org/I158842170"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":4.2459,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.9402138,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"4","issue":"1","first_page":"85","last_page":"96"},"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":0.9961000084877014,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9753000140190125,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.651383638381958},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.649712085723877},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.615542471408844},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.5975368022918701},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5729421377182007},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5710972547531128},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.5464911460876465},{"id":"https://openalex.org/keywords/perturbation-function","display_name":"Perturbation function","score":0.5446140766143799},{"id":"https://openalex.org/keywords/vector-optimization","display_name":"Vector optimization","score":0.4883818030357361},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4773328900337219},{"id":"https://openalex.org/keywords/dual-space","display_name":"Dual space","score":0.4721895456314087},{"id":"https://openalex.org/keywords/wolfe-duality","display_name":"Wolfe duality","score":0.4421873986721039},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.34821993112564087},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.3425494432449341},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.32487326860427856},{"id":"https://openalex.org/keywords/weak-duality","display_name":"Weak duality","score":0.31291067600250244},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.29918956756591797},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1857738494873047}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.651383638381958},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.649712085723877},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.615542471408844},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.5975368022918701},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5729421377182007},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5710972547531128},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.5464911460876465},{"id":"https://openalex.org/C102144036","wikidata":"https://www.wikidata.org/wiki/Q7170952","display_name":"Perturbation function","level":5,"score":0.5446140766143799},{"id":"https://openalex.org/C164088818","wikidata":"https://www.wikidata.org/wiki/Q7917833","display_name":"Vector optimization","level":4,"score":0.4883818030357361},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4773328900337219},{"id":"https://openalex.org/C45633534","wikidata":"https://www.wikidata.org/wiki/Q752487","display_name":"Dual space","level":2,"score":0.4721895456314087},{"id":"https://openalex.org/C109456813","wikidata":"https://www.wikidata.org/wiki/Q8029991","display_name":"Wolfe duality","level":5,"score":0.4421873986721039},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.34821993112564087},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3425494432449341},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.32487326860427856},{"id":"https://openalex.org/C80682859","wikidata":"https://www.wikidata.org/wiki/Q7977943","display_name":"Weak duality","level":4,"score":0.31291067600250244},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.29918956756591797},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1857738494873047},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11590-009-0141-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-009-0141-x","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"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":"Optimization Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W19249476","https://openalex.org/W196143036","https://openalex.org/W1512422500","https://openalex.org/W1580873762","https://openalex.org/W1599607462","https://openalex.org/W1963909982","https://openalex.org/W1980518765","https://openalex.org/W1995895880","https://openalex.org/W2007250169","https://openalex.org/W2011433961","https://openalex.org/W2034976213","https://openalex.org/W2035458531","https://openalex.org/W2041363761","https://openalex.org/W2045774013","https://openalex.org/W2073718458","https://openalex.org/W2081258360","https://openalex.org/W2092083685","https://openalex.org/W2121051620","https://openalex.org/W2166889871","https://openalex.org/W2423508375","https://openalex.org/W3206064939"],"related_works":["https://openalex.org/W4313014939","https://openalex.org/W4210245775","https://openalex.org/W2241982889","https://openalex.org/W2097707778","https://openalex.org/W4224273196","https://openalex.org/W3139624985","https://openalex.org/W2162423280","https://openalex.org/W578535666","https://openalex.org/W2021335455","https://openalex.org/W3168285647"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}