{"id":"https://openalex.org/W4214509979","doi":"https://doi.org/10.1142/s0217595922500099","title":"Scalarization and Optimality Conditions of <i>E</i>-Globally Proper Efficient Solution for Set-Valued Equilibrium Problems","display_name":"Scalarization and Optimality Conditions of <i>E</i>-Globally Proper Efficient Solution for Set-Valued Equilibrium Problems","publication_year":2022,"publication_date":"2022-02-28","ids":{"openalex":"https://openalex.org/W4214509979","doi":"https://doi.org/10.1142/s0217595922500099"},"language":"en","primary_location":{"id":"doi:10.1142/s0217595922500099","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0217595922500099","pdf_url":null,"source":{"id":"https://openalex.org/S1254427","display_name":"Asia Pacific Journal of Operational Research","issn_l":"0217-5959","issn":["0217-5959","1793-7019"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asia-Pacific Journal of Operational Research","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/A5061539112","display_name":"Zhiang Zhou","orcid":"https://orcid.org/0000-0002-8054-4176"},"institutions":[{"id":"https://openalex.org/I50632499","display_name":"Chongqing University of Technology","ror":"https://ror.org/04vgbd477","country_code":"CN","type":"education","lineage":["https://openalex.org/I50632499"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhi-Ang Zhou","raw_affiliation_strings":["College of Science, Chongqing University of Technology, Chongqing 400054, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Chongqing University of Technology, Chongqing 400054, P. R. China","institution_ids":["https://openalex.org/I50632499"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102406015","display_name":"Min Kuang","orcid":null},"institutions":[{"id":"https://openalex.org/I50632499","display_name":"Chongqing University of Technology","ror":"https://ror.org/04vgbd477","country_code":"CN","type":"education","lineage":["https://openalex.org/I50632499"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Min Kuang","raw_affiliation_strings":["College of Science, Chongqing University of Technology, Chongqing 400054, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Chongqing University of Technology, Chongqing 400054, P. R. China","institution_ids":["https://openalex.org/I50632499"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I50632499"],"apc_list":null,"apc_paid":null,"fwci":0.7612,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.73088562,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"40","issue":"02","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":0.9998999834060669,"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":0.989300012588501,"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":0.9871000051498413,"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/hausdorff-space","display_name":"Hausdorff space","score":0.6989263892173767},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6914415955543518},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6683204770088196},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6105643510818481},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5666443705558777},{"id":"https://openalex.org/keywords/solution-set","display_name":"Solution set","score":0.5012087821960449},{"id":"https://openalex.org/keywords/feasible-region","display_name":"Feasible region","score":0.4651433229446411},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3611389994621277},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.35844123363494873},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22977092862129211},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.139646977186203}],"concepts":[{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.6989263892173767},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6914415955543518},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6683204770088196},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6105643510818481},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5666443705558777},{"id":"https://openalex.org/C60033838","wikidata":"https://www.wikidata.org/wiki/Q1751685","display_name":"Solution set","level":3,"score":0.5012087821960449},{"id":"https://openalex.org/C177067428","wikidata":"https://www.wikidata.org/wiki/Q17013331","display_name":"Feasible region","level":2,"score":0.4651433229446411},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3611389994621277},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.35844123363494873},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22977092862129211},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.139646977186203},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0217595922500099","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0217595922500099","pdf_url":null,"source":{"id":"https://openalex.org/S1254427","display_name":"Asia Pacific Journal of Operational Research","issn_l":"0217-5959","issn":["0217-5959","1793-7019"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asia-Pacific Journal of Operational Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:wsi:apjorx:v:40:y:2023:i:02:n:s0217595922500099","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S0217595922500099","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2956562311","display_name":null,"funder_award_id":"12171061","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W19033009","https://openalex.org/W1969411229","https://openalex.org/W1991256352","https://openalex.org/W2020860144","https://openalex.org/W2040990300","https://openalex.org/W2057447513","https://openalex.org/W2061662972","https://openalex.org/W2072886676","https://openalex.org/W2079936218","https://openalex.org/W2093737083","https://openalex.org/W2095387334","https://openalex.org/W2133559997","https://openalex.org/W2294394507","https://openalex.org/W2467773526","https://openalex.org/W2594871394","https://openalex.org/W2884171652","https://openalex.org/W3032822599","https://openalex.org/W3146014150","https://openalex.org/W4235864991"],"related_works":["https://openalex.org/W2392413043","https://openalex.org/W930615311","https://openalex.org/W1977310087","https://openalex.org/W2057305555","https://openalex.org/W2041712909","https://openalex.org/W1999486572","https://openalex.org/W2036801487","https://openalex.org/W2063660181","https://openalex.org/W2351338075","https://openalex.org/W4283325509"],"abstract_inverted_index":{"In":[0],"this":[1,105],"paper,":[2],"our":[3,99],"purpose":[4],"is":[5,44],"to":[6,11,97],"use":[7],"the":[8,13,24,31,53,66,71,86,114],"improvement":[9],"set":[10],"investigate":[12],"scalarization":[14,55],"and":[15,73,108],"optimality":[16,75],"conditions":[17,76],"of":[18,33,57,68,88],"E-globally":[19,34,58,89],"proper":[20,35,59,90],"efficient":[21,36,60],"solution":[22,37,61],"for":[23,38,77],"set-valued":[25,39,78],"equilibrium":[26,40,79],"problems":[27,41,80],"with":[28,42,81],"constraints.":[29],"First,":[30],"notion":[32],"constraints":[43,82],"introduced":[45],"in":[46,85,104,113],"locally":[47],"convex":[48],"Hausdorff":[49],"topological":[50],"spaces.":[51],"Second,":[52],"linear":[54],"theorems":[56],"are":[62,83],"derived.":[63],"Finally,":[64],"under":[65],"assumption":[67],"nearly":[69],"E-subconvexlikeness,":[70],"Kuhn\u2013Tucker":[72],"Lagrange":[74],"obtained":[84,103],"sense":[87],"efficiency.":[91],"Meanwhile,":[92],"we":[93],"give":[94],"some":[95,110],"examples":[96],"illustrate":[98],"results.":[100],"The":[101],"results":[102,112],"paper":[106],"improve":[107],"generalize":[109],"known":[111],"literature.":[115]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}