{"id":"https://openalex.org/W3014859321","doi":"https://doi.org/10.1007/s10957-020-01657-2","title":"Convergence of Solutions to Set Optimization Problems with the Set Less Order Relation","display_name":"Convergence of Solutions to Set Optimization Problems with the Set Less Order Relation","publication_year":2020,"publication_date":"2020-03-30","ids":{"openalex":"https://openalex.org/W3014859321","doi":"https://doi.org/10.1007/s10957-020-01657-2","mag":"3014859321"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-020-01657-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-020-01657-2","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory 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/A5112022963","display_name":"L\u00e2m Qu\u1ed1c Anh","orcid":null},"institutions":[{"id":"https://openalex.org/I177733328","display_name":"Can Tho University","ror":"https://ror.org/0071qz696","country_code":"VN","type":"education","lineage":["https://openalex.org/I177733328"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Lam Quoc Anh","raw_affiliation_strings":["Department of Mathematics, Teacher College, Cantho University, Can Tho, Vietnam"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Teacher College, Cantho University, Can Tho, Vietnam","institution_ids":["https://openalex.org/I177733328"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011393970","display_name":"Tran Quoc Duy","orcid":"https://orcid.org/0000-0001-9524-4179"},"institutions":[{"id":"https://openalex.org/I141445968","display_name":"Ton Duc Thang University","ror":"https://ror.org/01drq0835","country_code":"VN","type":"education","lineage":["https://openalex.org/I141445968"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Tran Quoc Duy","raw_affiliation_strings":["Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam","Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam"],"affiliations":[{"raw_affiliation_string":"Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I141445968"]},{"raw_affiliation_string":"Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I141445968"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085462562","display_name":"Dinh Vinh Hien","orcid":null},"institutions":[{"id":"https://openalex.org/I4210116271","display_name":"Ho Chi Minh City University of Industry and Trade","ror":"https://ror.org/02b2dfs85","country_code":"VN","type":"education","lineage":["https://openalex.org/I4210116271"]},{"id":"https://openalex.org/I123565023","display_name":"Vietnam National University Ho Chi Minh City","ror":"https://ror.org/00waaqh38","country_code":"VN","type":"education","lineage":["https://openalex.org/I123565023"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Dinh Vinh Hien","raw_affiliation_strings":["Department of Mathematics, Ho Chi Minh City University of Food Industry, Ho Chi Minh City, Vietnam","Faculty of Mathematics and Computer Science, University of Science, Vietnam National University Ho Chi Minh City, Ho Chi Minh City, Vietnam"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ho Chi Minh City University of Food Industry, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I4210116271"]},{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, University of Science, Vietnam National University Ho Chi Minh City, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I123565023"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046487937","display_name":"Daishi Kuroiwa","orcid":null},"institutions":[{"id":"https://openalex.org/I169016828","display_name":"Shimane University","ror":"https://ror.org/01jaaym28","country_code":"JP","type":"education","lineage":["https://openalex.org/I169016828"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Daishi Kuroiwa","raw_affiliation_strings":["Department of Mathematics, Shimane University, Matsue, Shimane, 690-8504, Japan","Department of Mathematics, Shimane University, Matsue, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shimane University, Matsue, Shimane, 690-8504, Japan","institution_ids":["https://openalex.org/I169016828"]},{"raw_affiliation_string":"Department of Mathematics, Shimane University, Matsue, Japan","institution_ids":["https://openalex.org/I169016828"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076530191","display_name":"Narin Petrot","orcid":"https://orcid.org/0000-0001-6539-7107"},"institutions":[{"id":"https://openalex.org/I66200439","display_name":"Naresuan University","ror":"https://ror.org/03e2qe334","country_code":"TH","type":"education","lineage":["https://openalex.org/I66200439"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Narin Petrot","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand","Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, Thailand"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand","institution_ids":["https://openalex.org/I66200439"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, Thailand","institution_ids":["https://openalex.org/I66200439"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5112022963"],"corresponding_institution_ids":["https://openalex.org/I177733328"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":3.1758,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.93322867,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"185","issue":"2","first_page":"416","last_page":"432"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9940000176429749,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9771000146865845,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.8203572034835815},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6591099500656128},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6420437097549438},{"id":"https://openalex.org/keywords/hausdorff-space","display_name":"Hausdorff space","score":0.6288052797317505},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.588646650314331},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.5560408234596252},{"id":"https://openalex.org/keywords/solution-set","display_name":"Solution set","score":0.5361563563346863},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5171241760253906},{"id":"https://openalex.org/keywords/hausdorff-distance","display_name":"Hausdorff distance","score":0.47929874062538147},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4781978130340576},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.47163864970207214},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45583462715148926},{"id":"https://openalex.org/keywords/vector-optimization","display_name":"Vector optimization","score":0.45449674129486084},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4490460157394409},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4182097911834717},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23939934372901917},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17302930355072021},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.1549150049686432},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1367795467376709}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8203572034835815},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6591099500656128},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6420437097549438},{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.6288052797317505},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.588646650314331},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.5560408234596252},{"id":"https://openalex.org/C60033838","wikidata":"https://www.wikidata.org/wiki/Q1751685","display_name":"Solution set","level":3,"score":0.5361563563346863},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5171241760253906},{"id":"https://openalex.org/C141898687","wikidata":"https://www.wikidata.org/wiki/Q1501997","display_name":"Hausdorff distance","level":2,"score":0.47929874062538147},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4781978130340576},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.47163864970207214},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45583462715148926},{"id":"https://openalex.org/C164088818","wikidata":"https://www.wikidata.org/wiki/Q7917833","display_name":"Vector optimization","level":4,"score":0.45449674129486084},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4490460157394409},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4182097911834717},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23939934372901917},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17302930355072021},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.1549150049686432},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1367795467376709},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"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/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-020-01657-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-020-01657-2","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:joptap:v:185:y:2020:i:2:d:10.1007_s10957-020-01657-2","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-020-01657-2","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W113278869","https://openalex.org/W1452367236","https://openalex.org/W1585268704","https://openalex.org/W2016429743","https://openalex.org/W2017942050","https://openalex.org/W2021229104","https://openalex.org/W2035138741","https://openalex.org/W2035990529","https://openalex.org/W2075625005","https://openalex.org/W2194600262","https://openalex.org/W2321794351","https://openalex.org/W2346414921","https://openalex.org/W2478963760","https://openalex.org/W2534725646","https://openalex.org/W2582528780","https://openalex.org/W2587774467","https://openalex.org/W2611395917","https://openalex.org/W2755488487","https://openalex.org/W2770060446","https://openalex.org/W2896281007","https://openalex.org/W2900639545","https://openalex.org/W2906529897","https://openalex.org/W3153352392","https://openalex.org/W4231758816"],"related_works":["https://openalex.org/W2138511311","https://openalex.org/W1144450175","https://openalex.org/W2031465436","https://openalex.org/W1512585147","https://openalex.org/W2072886676","https://openalex.org/W3037607774","https://openalex.org/W1989726050","https://openalex.org/W1991371429","https://openalex.org/W1988098345","https://openalex.org/W2365724145"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}