{"id":"https://openalex.org/W7213398166","doi":"https://doi.org/10.48550/arxiv.2609.16703","title":"Stability Analysis of Generalized Multi-Source Weber Problems","display_name":"Stability Analysis of Generalized Multi-Source Weber Problems","publication_year":2026,"publication_date":"2026-09-15","ids":{"openalex":"https://openalex.org/W7213398166","doi":"https://doi.org/10.48550/arxiv.2609.16703"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.16703","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16703","pdf_url":"https://arxiv.org/pdf/2609.16703","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.16703","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153501704","display_name":"N. H. Hai","orcid":null,"observed_orcids":[]},"institutions":[{"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"]},{"id":"https://openalex.org/I23582244","display_name":"Ho Chi Minh City University of Science","ror":"https://ror.org/05jfbgm49","country_code":"VN","type":"education","lineage":["https://openalex.org/I123565023","https://openalex.org/I23582244"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Hai, N. H.","raw_affiliation_strings":["Faculty of Mathematics and Computer Science , University of Science , Ho Chi Minh City , Vietnam","Vietnam National University , Ho Chi Minh City , Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science , University of Science , Ho Chi Minh City , Vietnam","institution_ids":["https://openalex.org/I23582244"]},{"raw_affiliation_string":"Vietnam National University , Ho Chi Minh City , Vietnam","institution_ids":["https://openalex.org/I123565023"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123857342","display_name":"V. S. T. Long","orcid":null,"observed_orcids":[]},"institutions":[{"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"]},{"id":"https://openalex.org/I23582244","display_name":"Ho Chi Minh City University of Science","ror":"https://ror.org/05jfbgm49","country_code":"VN","type":"education","lineage":["https://openalex.org/I123565023","https://openalex.org/I23582244"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Long, V. S. T.","raw_affiliation_strings":["Faculty of Mathematics and Computer Science , University of Science , Ho Chi Minh City , Vietnam","Vietnam National University , Ho Chi Minh City , Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science , University of Science , Ho Chi Minh City , Vietnam","institution_ids":["https://openalex.org/I23582244"]},{"raw_affiliation_string":"Vietnam National University , Ho Chi Minh City , Vietnam","institution_ids":["https://openalex.org/I123565023"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123845451","display_name":"N. M. Nam","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I126345244","display_name":"Portland State University","ror":"https://ror.org/00yn2fy02","country_code":"US","type":"education","lineage":["https://openalex.org/I126345244"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nam, N. M.","raw_affiliation_strings":["Fariborz Maseeh Department of Mathematics and Statistics , Portland State University , Portland , OR 97207 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fariborz Maseeh Department of Mathematics and Statistics , Portland State University , Portland , OR 97207 , USA","institution_ids":["https://openalex.org/I126345244"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006470235","display_name":"N. D. Yen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210148301","display_name":"Institute of Mathematics","ror":"https://ror.org/04jr71r83","country_code":"VN","type":"facility","lineage":["https://openalex.org/I4210148301","https://openalex.org/I70349855"]},{"id":"https://openalex.org/I70349855","display_name":"Vietnam Academy of Science and Technology","ror":"https://ror.org/02wsd5p50","country_code":"VN","type":"government","lineage":["https://openalex.org/I70349855"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Yen, N. D.","raw_affiliation_strings":["Institute of Mathematics , Vietnam Academy of Science and Technology , 18 Hoang Quoc Viet , Hanoi 10307 , Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics , Vietnam Academy of Science and Technology , 18 Hoang Quoc Viet , Hanoi 10307 , Vietnam","institution_ids":["https://openalex.org/I4210148301","https://openalex.org/I70349855"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.9477999806404114,"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":0.9477999806404114,"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/T11502","display_name":"Facility Location and Emergency Management","score":0.025800000876188278,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.007199999876320362,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stability-analysis","display_name":"stability analysis","score":0.8650000095367432},{"id":"https://openalex.org/keywords/data-perturbation","display_name":"data perturbation","score":0.949999988079071},{"id":"https://openalex.org/keywords/minkowski-function","display_name":"Minkowski function","score":0.9660000205039978},{"id":"https://openalex.org/keywords/lipschitz-constant","display_name":"Lipschitz constant","score":0.8560000061988831},{"id":"https://openalex.org/keywords/optimal-value-function","display_name":"optimal value function","score":0.8989999890327454},{"id":"https://openalex.org/keywords/upper-semicontinuity","display_name":"upper semicontinuity","score":0.9879999756813049},{"id":"https://openalex.org/keywords/facility-location","display_name":"facility location","score":0.515999972820282}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.819100022315979},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6625999808311462},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6377000212669373},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5620999932289124},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4629000127315521},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.384799987077713},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37369999289512634},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32519999146461487},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2888000011444092},{"id":"https://openalex.org/C143170015","wikidata":"https://www.wikidata.org/wiki/Q17007850","display_name":"Stability conditions","level":3,"score":0.28690001368522644},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.26080000400543213},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2605000138282776}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.16703","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16703","pdf_url":"https://arxiv.org/pdf/2609.16703","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"doi:10.48550/arxiv.2609.16703","doi":"https://doi.org/10.48550/arxiv.2609.16703","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.16703","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.16703","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16703","pdf_url":"https://arxiv.org/pdf/2609.16703","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213398166.pdf","grobid_xml":"https://content.openalex.org/works/W7213398166.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7171987082","https://openalex.org/W2129181728","https://openalex.org/W2004199696","https://openalex.org/W2009624847","https://openalex.org/W4403780000","https://openalex.org/W2904246568","https://openalex.org/W4292336384","https://openalex.org/W2073159007","https://openalex.org/W100441194","https://openalex.org/W6944745137"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3],"stability":[4,87],"analysis":[5],"of":[6,15,21,44,59,67,88,93],"the":[7,13,19,22,32,45,56,64,86,94],"generalized":[8],"multi-source":[9],"Weber":[10],"problems":[11,96],"under":[12],"influence":[14],"data":[16],"perturbation":[17],"within":[18],"framework":[20],"Minkowski":[23],"function.":[24],"First,":[25],"we":[26,40,51],"establish":[27],"explicit":[28],"Lipschitz":[29],"constants":[30],"for":[31,55],"objective":[33],"functions":[34],"and":[35,63],"optimal":[36,47,90],"value":[37],"functions.":[38],"Then,":[39],"prove":[41],"several":[42,82],"properties":[43],"global":[46,60],"solution":[48,61,69,91],"sets.":[49],"Furthermore,":[50],"provide":[52],"sufficient":[53],"conditions":[54],"upper":[57],"semicontinuity":[58,66],"mappings":[62,92],"inner":[65],"local":[68,89],"mappings.":[70],"Three":[71],"illustrative":[72],"examples":[73],"are":[74],"constructed.":[75],"Our":[76],"results":[77],"give":[78],"indirect":[79],"answers":[80],"to":[81],"open":[83],"questions":[84],"regarding":[85],"optimization":[95],"discussed.":[97]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-17T00:00:00"}
