{"id":"https://openalex.org/W2467773526","doi":"https://doi.org/10.1080/10556788.2016.1200043","title":"Vector equilibrium problems under improvement sets and linear scalarization with stability applications","display_name":"Vector equilibrium problems under improvement sets and linear scalarization with stability applications","publication_year":2016,"publication_date":"2016-07-07","ids":{"openalex":"https://openalex.org/W2467773526","doi":"https://doi.org/10.1080/10556788.2016.1200043","mag":"2467773526"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2016.1200043","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2016.1200043","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","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/A5011627130","display_name":"Chun-Rong Chen","orcid":"https://orcid.org/0000-0001-8285-7881"},"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":"Chun-Rong Chen","raw_affiliation_strings":["College of Mathematics and Statistics, Chongqing University, Chongqing, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Chongqing University, Chongqing, People's Republic of China","institution_ids":["https://openalex.org/I158842170"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101680582","display_name":"Xin Zuo","orcid":"https://orcid.org/0000-0002-3978-6886"},"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":"Xin Zuo","raw_affiliation_strings":["College of Mathematics and Statistics, Chongqing University, Chongqing, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Chongqing University, Chongqing, People's Republic of China","institution_ids":["https://openalex.org/I158842170"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052322735","display_name":"Fang L\u00fc","orcid":"https://orcid.org/0000-0003-2727-2658"},"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":"Fang Lu","raw_affiliation_strings":["College of Mathematics and Statistics, Chongqing University, Chongqing, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Chongqing University, Chongqing, People's Republic of China","institution_ids":["https://openalex.org/I158842170"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111597009","display_name":"Shengjie 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":false,"raw_author_name":"Sheng-Jie Li","raw_affiliation_strings":["College of Mathematics and Statistics, Chongqing University, Chongqing, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Chongqing University, Chongqing, People's Republic of China","institution_ids":["https://openalex.org/I158842170"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5011627130"],"corresponding_institution_ids":["https://openalex.org/I158842170"],"apc_list":null,"apc_paid":null,"fwci":1.7559,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.86165464,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"31","issue":"6","first_page":"1240","last_page":"1257"},"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/T12137","display_name":"Economic theories and models","score":0.9921000003814697,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9653000235557556,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.6371216177940369},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6127720475196838},{"id":"https://openalex.org/keywords/vector-optimization","display_name":"Vector optimization","score":0.6017249822616577},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5649818778038025},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5529140830039978},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49008047580718994},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38129764795303345},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.35584723949432373},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.07718512415885925},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.052113503217697144}],"concepts":[{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.6371216177940369},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6127720475196838},{"id":"https://openalex.org/C164088818","wikidata":"https://www.wikidata.org/wiki/Q7917833","display_name":"Vector optimization","level":4,"score":0.6017249822616577},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5649818778038025},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5529140830039978},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49008047580718994},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38129764795303345},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.35584723949432373},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.07718512415885925},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.052113503217697144},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556788.2016.1200043","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2016.1200043","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1758622557","display_name":null,"funder_award_id":"11171362,11301567,11571055","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4265054652","display_name":null,"funder_award_id":"106112015CDJXY100002","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W67294476","https://openalex.org/W360991825","https://openalex.org/W596285643","https://openalex.org/W1484024929","https://openalex.org/W1966839439","https://openalex.org/W1983025619","https://openalex.org/W1986517159","https://openalex.org/W1987556385","https://openalex.org/W1991256352","https://openalex.org/W1996631695","https://openalex.org/W1996810073","https://openalex.org/W2005341901","https://openalex.org/W2032878137","https://openalex.org/W2046337994","https://openalex.org/W2052770754","https://openalex.org/W2056578149","https://openalex.org/W2061662972","https://openalex.org/W2062679376","https://openalex.org/W2072886676","https://openalex.org/W2077546098","https://openalex.org/W2083207585","https://openalex.org/W2083818478","https://openalex.org/W2087625147","https://openalex.org/W2098467864","https://openalex.org/W2154078976","https://openalex.org/W2163042361","https://openalex.org/W2481311888","https://openalex.org/W2595644070","https://openalex.org/W4231758816"],"related_works":["https://openalex.org/W2565276936","https://openalex.org/W2766340440","https://openalex.org/W4385713703","https://openalex.org/W109016340","https://openalex.org/W188711498","https://openalex.org/W2390455111","https://openalex.org/W3199277564","https://openalex.org/W2184300223","https://openalex.org/W2146329574","https://openalex.org/W1992731528"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"for":[3,26],"vector":[4,27,55],"equilibrium":[5],"problems":[6,29,51,69],"where":[7],"the":[8,23,31,38],"ordering":[9],"relations":[10],"are":[11,19,60,70],"defined":[12],"via":[13],"improvement":[14,58],"sets,":[15],"linear":[16],"scalarization":[17,63],"characterizations":[18],"established,":[20],"which":[21],"include":[22],"well-known":[24],"ones":[25],"optimization":[28],"in":[30],"literature":[32],"as":[33],"special":[34],"cases.":[35],"By":[36],"applying":[37],"obtained":[39],"results,":[40],"some":[41],"continuity":[42],"(both":[43],"lower":[44],"and":[45],"upper":[46],"semicontinuities)":[47],"conclusions":[48],"of":[49],"parametric":[50],"with":[52],"respect":[53],"to":[54],"equilibria":[56],"through":[57],"sets":[59],"deduced":[61],"using":[62],"approaches.":[64],"Several":[65],"unsolved":[66],"or":[67],"interesting":[68],"also":[71],"proposed.":[72]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}