{"id":"https://openalex.org/W4392018686","doi":"https://doi.org/10.1080/10556788.2024.2318707","title":"Bilevel optimization with a multi-objective lower-level problem: risk-neutral and risk-averse formulations","display_name":"Bilevel optimization with a multi-objective lower-level problem: risk-neutral and risk-averse formulations","publication_year":2024,"publication_date":"2024-02-20","ids":{"openalex":"https://openalex.org/W4392018686","doi":"https://doi.org/10.1080/10556788.2024.2318707"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2024.2318707","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1080/10556788.2024.2318707","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","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/A5042143914","display_name":"Tommaso Giovannelli","orcid":"https://orcid.org/0000-0002-1436-5348"},"institutions":[{"id":"https://openalex.org/I186143895","display_name":"Lehigh University","ror":"https://ror.org/012afjb06","country_code":"US","type":"education","lineage":["https://openalex.org/I186143895"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"T. Giovannelli","raw_affiliation_strings":["Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA","institution_ids":["https://openalex.org/I186143895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079967989","display_name":"G. D. Kent","orcid":"https://orcid.org/0009-0003-8636-0348"},"institutions":[{"id":"https://openalex.org/I186143895","display_name":"Lehigh University","ror":"https://ror.org/012afjb06","country_code":"US","type":"education","lineage":["https://openalex.org/I186143895"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"G. D. Kent","raw_affiliation_strings":["Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA","institution_ids":["https://openalex.org/I186143895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045737795","display_name":"L. N. Vicente","orcid":"https://orcid.org/0000-0003-1097-6384"},"institutions":[{"id":"https://openalex.org/I186143895","display_name":"Lehigh University","ror":"https://ror.org/012afjb06","country_code":"US","type":"education","lineage":["https://openalex.org/I186143895"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"L. N. Vicente","raw_affiliation_strings":["Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA","institution_ids":["https://openalex.org/I186143895"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5042143914"],"corresponding_institution_ids":["https://openalex.org/I186143895"],"apc_list":null,"apc_paid":null,"fwci":0.5344,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.63350812,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"39","issue":"4","first_page":"756","last_page":"778"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9987999796867371,"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"}},"topics":[{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9987999796867371,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9922999739646912,"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":0.9850000143051147,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bilevel-optimization","display_name":"Bilevel optimization","score":0.8096233606338501},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7202954292297363},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.5757263898849487},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5393490791320801},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.41926106810569763},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3860837519168854}],"concepts":[{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.8096233606338501},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7202954292297363},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.5757263898849487},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5393490791320801},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.41926106810569763},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3860837519168854}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556788.2024.2318707","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1080/10556788.2024.2318707","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5354348299","display_name":null,"funder_award_id":"FA9550-23-1-0217","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W115287288","https://openalex.org/W147998453","https://openalex.org/W2002511953","https://openalex.org/W2016969860","https://openalex.org/W2049748902","https://openalex.org/W2052471135","https://openalex.org/W2058637990","https://openalex.org/W2060727197","https://openalex.org/W2071707442","https://openalex.org/W2100717205","https://openalex.org/W2111999692","https://openalex.org/W2116775748","https://openalex.org/W2143185749","https://openalex.org/W2153015072","https://openalex.org/W2595897327","https://openalex.org/W2614367549","https://openalex.org/W2885943512","https://openalex.org/W2914195244","https://openalex.org/W2952308123","https://openalex.org/W2957161181","https://openalex.org/W2963433607","https://openalex.org/W3003257820","https://openalex.org/W3080795007","https://openalex.org/W3110321216","https://openalex.org/W3136031552","https://openalex.org/W3165794802","https://openalex.org/W4292864963","https://openalex.org/W4300448178","https://openalex.org/W4302557773"],"related_works":["https://openalex.org/W4318070895","https://openalex.org/W3157915181","https://openalex.org/W4401134013","https://openalex.org/W2896140431","https://openalex.org/W4287330080","https://openalex.org/W1994436307","https://openalex.org/W3127438322","https://openalex.org/W2795565301","https://openalex.org/W4285677055","https://openalex.org/W2216231335"],"abstract_inverted_index":{"In":[0,100],"this":[1,101],"work,":[2],"we":[3,103],"propose":[4],"different":[5,65],"formulations":[6],"and":[7,12,33,53,107,115,120],"gradient-based":[8,122],"algorithms":[9],"for":[10,50,85],"deterministic":[11,31,87,119],"stochastic":[13,40,48,121],"bilevel":[14,58],"problems":[15,24,59],"with":[16,60],"conflicting":[17],"objectives":[18],"in":[19,29,47],"the":[20,30,44,72,75,86,92,117],"lower":[21,63],"level.":[22],"Such":[23],"have":[25,34],"received":[26],"little":[27],"attention":[28],"case":[32,88],"never":[35],"been":[36],"studied":[37],"from":[38],"a":[39,61],"approximation":[41],"viewpoint":[42],"despite":[43],"recent":[45],"advances":[46],"methods":[49],"single-level,":[51],"bilevel,":[52],"multi-objective":[54,62],"optimization.":[55],"To":[56],"solve":[57],"level,":[64],"approaches":[66],"can":[67],"be":[68],"considered":[69],"depending":[70],"on":[71],"interpretation":[73],"of":[74,90],"lower-level":[76,98],"optimality.":[77],"An":[78],"optimistic":[79],"formulation":[80],"that":[81],"was":[82],"previously":[83],"introduced":[84],"consists":[89],"minimizing":[91],"upper-level":[93],"function":[94],"over":[95],"all":[96],"non-dominated":[97],"solutions.":[99],"paper,":[102],"develop":[104,116],"new":[105],"risk-neutral":[106],"risk-averse":[108],"formulations,":[109],"address":[110],"their":[111],"main":[112],"computational":[113],"challenges,":[114],"corresponding":[118],"algorithms.":[123]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2025-12-21T01:58:51.020947","created_date":"2025-10-10T00:00:00"}