{"id":"https://openalex.org/W4403501920","doi":"https://doi.org/10.1007/s10898-024-01438-5","title":"Unboundedness of the images of set-valued mappings having closed graphs: application to vector optimization","display_name":"Unboundedness of the images of set-valued mappings having closed graphs: application to vector optimization","publication_year":2024,"publication_date":"2024-10-18","ids":{"openalex":"https://openalex.org/W4403501920","doi":"https://doi.org/10.1007/s10898-024-01438-5"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-024-01438-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-024-01438-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-024-01438-5.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10898-024-01438-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072449986","display_name":"Vu Trung Hieu","orcid":"https://orcid.org/0000-0001-5775-9788"},"institutions":[{"id":"https://openalex.org/I204778367","display_name":"Norwegian University of Science and Technology","ror":"https://ror.org/05xg72x27","country_code":"NO","type":"education","lineage":["https://openalex.org/I204778367"]},{"id":"https://openalex.org/I4210126580","display_name":"RIKEN Center for Advanced Intelligence Project","ror":"https://ror.org/03ckxwf91","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652","https://openalex.org/I4210126580"]}],"countries":["JP","NO"],"is_corresponding":true,"raw_author_name":"V. T. Hieu","raw_affiliation_strings":["Center for Advanced Intelligence Project, RIKEN, Tokyo, 103-0027, Japan","Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491, Trondheim, Norway"],"raw_orcid":"https://orcid.org/0000-0001-5775-9788","affiliations":[{"raw_affiliation_string":"Center for Advanced Intelligence Project, RIKEN, Tokyo, 103-0027, Japan","institution_ids":["https://openalex.org/I4210126580"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491, Trondheim, Norway","institution_ids":["https://openalex.org/I204778367"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016712684","display_name":"Elisabeth K\u00f6bis","orcid":"https://orcid.org/0000-0003-3842-4522"},"institutions":[{"id":"https://openalex.org/I204778367","display_name":"Norwegian University of Science and Technology","ror":"https://ror.org/05xg72x27","country_code":"NO","type":"education","lineage":["https://openalex.org/I204778367"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"E. A. S. K\u00f6bis","raw_affiliation_strings":["Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491, Trondheim, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491, Trondheim, Norway","institution_ids":["https://openalex.org/I204778367"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046338741","display_name":"Markus A. K\u00f6bis","orcid":null},"institutions":[{"id":"https://openalex.org/I204778367","display_name":"Norwegian University of Science and Technology","ror":"https://ror.org/05xg72x27","country_code":"NO","type":"education","lineage":["https://openalex.org/I204778367"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"M. A. K\u00f6bis","raw_affiliation_strings":["Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491, Trondheim, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491, Trondheim, Norway","institution_ids":["https://openalex.org/I204778367"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074581587","display_name":"Paul Schmolling","orcid":"https://orcid.org/0009-0008-4157-0903"},"institutions":[{"id":"https://openalex.org/I204778367","display_name":"Norwegian University of Science and Technology","ror":"https://ror.org/05xg72x27","country_code":"NO","type":"education","lineage":["https://openalex.org/I204778367"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"P. H. Schm\u00f6lling","raw_affiliation_strings":["Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491, Trondheim, Norway"],"raw_orcid":"https://orcid.org/0009-0008-4157-0903","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491, Trondheim, Norway","institution_ids":["https://openalex.org/I204778367"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5072449986"],"corresponding_institution_ids":["https://openalex.org/I204778367","https://openalex.org/I4210126580"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2780},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.21317384,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"91","issue":"1","first_page":"217","last_page":"234"},"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":0.996999979019165,"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":0.9771999716758728,"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":0.8841463327407837},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5739008784294128},{"id":"https://openalex.org/keywords/vector-optimization","display_name":"Vector optimization","score":0.5546436309814453},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.395664244890213},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3559609651565552},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08808907866477966},{"id":"https://openalex.org/keywords/multi-swarm-optimization","display_name":"Multi-swarm optimization","score":0.06046631932258606}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8841463327407837},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5739008784294128},{"id":"https://openalex.org/C164088818","wikidata":"https://www.wikidata.org/wiki/Q7917833","display_name":"Vector optimization","level":4,"score":0.5546436309814453},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.395664244890213},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3559609651565552},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08808907866477966},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.06046631932258606},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10898-024-01438-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-024-01438-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-024-01438-5.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:jglopt:v:91:y:2025:i:1:d:10.1007_s10898-024-01438-5","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10898-024-01438-5","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":{"id":"doi:10.1007/s10898-024-01438-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-024-01438-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-024-01438-5.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311040","display_name":"Norges Teknisk-Naturvitenskapelige Universitet","ror":"https://ror.org/05xg72x27"},{"id":"https://openalex.org/F4320320885","display_name":"European Research Consortium for Informatics and Mathematics","ror":"https://ror.org/055zrhj18"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4403501920.pdf","grobid_xml":"https://content.openalex.org/works/W4403501920.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W580431932","https://openalex.org/W1499439642","https://openalex.org/W1585205451","https://openalex.org/W1967557454","https://openalex.org/W1974940125","https://openalex.org/W1997529087","https://openalex.org/W1997662222","https://openalex.org/W2061662972","https://openalex.org/W2074395742","https://openalex.org/W2092663189","https://openalex.org/W2093962623","https://openalex.org/W2339319209","https://openalex.org/W2342810421","https://openalex.org/W2540466932","https://openalex.org/W2626819135","https://openalex.org/W2765480842","https://openalex.org/W2794370287","https://openalex.org/W2901924265","https://openalex.org/W2963292098","https://openalex.org/W3103378461","https://openalex.org/W3195250998","https://openalex.org/W4206983496","https://openalex.org/W4241229021","https://openalex.org/W4249125060","https://openalex.org/W4302557773","https://openalex.org/W4307400846","https://openalex.org/W4396960891","https://openalex.org/W6629799166"],"related_works":["https://openalex.org/W2565276936","https://openalex.org/W2766340440","https://openalex.org/W4385713703","https://openalex.org/W4384574993","https://openalex.org/W109016340","https://openalex.org/W188711498","https://openalex.org/W2390455111","https://openalex.org/W3199277564","https://openalex.org/W4230074750","https://openalex.org/W1992731528"],"abstract_inverted_index":{"Abstract":[0],"In":[1,64],"this":[2],"paper,":[3],"we":[4,66,92],"propose":[5],"criteria":[6,35,95],"for":[7,88],"unboundedness":[8],"of":[9,12,42,56,72],"the":[10,54,70,80,100],"images":[11,55],"set-valued":[13],"mappings":[14,24,58],"having":[15],"closed":[16],"graphs":[17],"in":[18,44],"Euclidean":[19],"spaces.":[20],"We":[21],"focus":[22],"on":[23],"whose":[25,30],"domains":[26],"are":[27,32],"non-closed":[28],"or":[29],"values":[31],"connected.":[33],"These":[34],"allow":[36],"us":[37],"to":[38,60,96],"see":[39],"structural":[40],"properties":[41],"solutions":[43],"vector":[45],"optimization,":[46],"where":[47],"solution":[48,57,75,83,103],"sets":[49],"can":[50],"be":[51],"considered":[52],"as":[53],"associated":[59],"specific":[61],"scalarization":[62],"methods.":[63],"particular,":[65],"prove":[67],"that":[68,98],"if":[69,99],"domain":[71],"a":[73,89],"certain":[74],"mapping":[76],"is":[77,85,105,111],"non-closed,":[78],"then":[79,107],"weak":[81,101],"Pareto":[82,102],"set":[84,104],"unbounded.":[86,112],"Furthermore,":[87],"quasi-convex":[90],"problem,":[91],"demonstrate":[93],"two":[94],"ensure":[97],"disconnected":[106],"each":[108],"connected":[109],"component":[110]},"counts_by_year":[],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}