{"id":"https://openalex.org/W4413802952","doi":"https://doi.org/10.1007/s10957-025-02790-6","title":"Generalized Robust Optimization using the Notion of Set-Valued Probability","display_name":"Generalized Robust Optimization using the Notion of Set-Valued Probability","publication_year":2025,"publication_date":"2025-08-29","ids":{"openalex":"https://openalex.org/W4413802952","doi":"https://doi.org/10.1007/s10957-025-02790-6","pmid":"https://pubmed.ncbi.nlm.nih.gov/40893806"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-025-02790-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-025-02790-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-025-02790-6.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10957-025-02790-6.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008833108","display_name":"Davide La Torre","orcid":"https://orcid.org/0000-0003-2776-0037"},"institutions":[{"id":"https://openalex.org/I181418319","display_name":"SKEMA Business School","ror":"https://ror.org/036h8vg94","country_code":"FR","type":"education","lineage":["https://openalex.org/I181418319"]},{"id":"https://openalex.org/I4210150884","display_name":"Fondation Sophia Antipolis","ror":"https://ror.org/05nkcfv27","country_code":"FR","type":"other","lineage":["https://openalex.org/I4210150884"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Davide La Torre","raw_affiliation_strings":["SKEMA Business School, Universit\u00e9 C\u00f4te d'Azur Sophia Antipolis Campus, Sophia Antipolis, France"],"affiliations":[{"raw_affiliation_string":"SKEMA Business School, Universit\u00e9 C\u00f4te d'Azur Sophia Antipolis Campus, Sophia Antipolis, France","institution_ids":["https://openalex.org/I181418319","https://openalex.org/I4210150884"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014370411","display_name":"Franklin Mendivil","orcid":"https://orcid.org/0000-0002-6690-813X"},"institutions":[{"id":"https://openalex.org/I92688161","display_name":"Acadia University","ror":"https://ror.org/00839we02","country_code":"CA","type":"education","lineage":["https://openalex.org/I92688161"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Franklin Mendivil","raw_affiliation_strings":["Department of Mathematics and Statistics, Acadia University, Wolfville, Nova Scotia Canada","Department of Mathematics and Statistics, Acadia University, Wolfville, Nova Scotia, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Acadia University, Wolfville, Nova Scotia Canada","institution_ids":["https://openalex.org/I92688161"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, Acadia University, Wolfville, Nova Scotia, Canada","institution_ids":["https://openalex.org/I92688161"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025711210","display_name":"Matteo Rocca","orcid":"https://orcid.org/0000-0002-5849-4731"},"institutions":[{"id":"https://openalex.org/I115752224","display_name":"University of Insubria","ror":"https://ror.org/00s409261","country_code":"IT","type":"education","lineage":["https://openalex.org/I115752224"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Matteo Rocca","raw_affiliation_strings":["Department of Economics, Universit\u00e1 degli Studi dell'Insubria, Varese, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Economics, Universit\u00e1 degli Studi dell'Insubria, Varese, Italy","institution_ids":["https://openalex.org/I115752224"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5025711210"],"corresponding_institution_ids":["https://openalex.org/I115752224"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.21155638,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"207","issue":"3","first_page":"64","last_page":"64"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7747220993041992},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6910925507545471},{"id":"https://openalex.org/keywords/robust-optimization","display_name":"Robust optimization","score":0.5277265310287476},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5160943865776062},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4995405673980713},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3465363383293152},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.34288090467453003},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2286866307258606},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16271641850471497}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7747220993041992},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6910925507545471},{"id":"https://openalex.org/C193254401","wikidata":"https://www.wikidata.org/wiki/Q2160088","display_name":"Robust optimization","level":2,"score":0.5277265310287476},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5160943865776062},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4995405673980713},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3465363383293152},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.34288090467453003},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2286866307258606},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16271641850471497},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10957-025-02790-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-025-02790-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-025-02790-6.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmid:40893806","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40893806","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of optimization theory and applications","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:12397130","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/12397130","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC12397130/pdf/10957_2025_Article_2790.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"J Optim Theory Appl","raw_type":"Text"},{"id":"pmh:oai:cris.unibo.it:11585/1035916","is_oa":true,"landing_page_url":"https://hdl.handle.net/11585/1035916","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:irinsubria.uninsubria.it:11383/2197472","is_oa":false,"landing_page_url":"https://hdl.handle.net/11383/2197472","pdf_url":null,"source":{"id":"https://openalex.org/S4377196351","display_name":"IrInSubria (University of Insubria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I115752224","host_organization_name":"University of Insubria","host_organization_lineage":["https://openalex.org/I115752224"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s10957-025-02790-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-025-02790-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-025-02790-6.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4412192556","display_name":null,"funder_award_id":"2019:05237","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4413802952.pdf","grobid_xml":"https://content.openalex.org/works/W4413802952.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W222274241","https://openalex.org/W1980263293","https://openalex.org/W1991890515","https://openalex.org/W2019291268","https://openalex.org/W2026883227","https://openalex.org/W2037468024","https://openalex.org/W2068361733","https://openalex.org/W2074403900","https://openalex.org/W2075087125","https://openalex.org/W2136145857","https://openalex.org/W2147544122","https://openalex.org/W2226385761","https://openalex.org/W2294586855","https://openalex.org/W2402412545","https://openalex.org/W2516131933","https://openalex.org/W2615737084","https://openalex.org/W2625295579","https://openalex.org/W3110436430","https://openalex.org/W3149133232","https://openalex.org/W4210427261","https://openalex.org/W4240043449","https://openalex.org/W4249513058","https://openalex.org/W4251616545"],"related_works":["https://openalex.org/W3005017983","https://openalex.org/W2205708137","https://openalex.org/W3182145356","https://openalex.org/W3212504317","https://openalex.org/W1988872022","https://openalex.org/W1992148254","https://openalex.org/W3028487898","https://openalex.org/W2302257968","https://openalex.org/W4295680010","https://openalex.org/W3035069654"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,15],"novel":[3],"concept":[4],"of":[5,11,28,58],"robustness":[6,57],"grounded":[7],"in":[8,67,93],"the":[9,25,56],"framework":[10,63],"set-valued":[12,38],"probabilities,":[13,39],"offering":[14],"unified":[16],"and":[17,50,74,88],"versatile":[18],"approach":[19],"to":[20],"tackling":[21],"challenges":[22],"associated":[23],"with":[24],"statistical":[26],"estimation":[27],"uncertain":[29],"or":[30],"unknown":[31],"probabilities.":[32],"By":[33],"employing":[34],"scalarization":[35],"techniques":[36],"for":[37,83],"we":[40,45],"derive":[41],"optimality":[42],"conditions.":[43],"Additionally,":[44],"establish":[46],"generalized":[47],"convexity":[48],"properties":[49],"stability":[51],"conditions,":[52],"which":[53],"further":[54],"underpin":[55],"our":[59],"approach.":[60],"This":[61],"comprehensive":[62],"finds":[64],"significant":[65],"applications":[66],"areas":[68],"such":[69],"as":[70],"financial":[71],"portfolio":[72],"management":[73],"risk":[75],"measure":[76],"theory,":[77],"where":[78],"it":[79],"provides":[80],"powerful":[81],"tools":[82],"addressing":[84],"uncertainty,":[85],"optimizing":[86],"decision-making,":[87],"ensuring":[89],"resilience":[90],"against":[91],"variability":[92],"probabilistic":[94],"models.":[95]},"counts_by_year":[],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}