{"id":"https://openalex.org/W4401134013","doi":"https://doi.org/10.1007/s10898-024-01422-z","title":"Robust bilevel optimization for near-optimal lower-level solutions","display_name":"Robust bilevel optimization for near-optimal lower-level solutions","publication_year":2024,"publication_date":"2024-07-30","ids":{"openalex":"https://openalex.org/W4401134013","doi":"https://doi.org/10.1007/s10898-024-01422-z"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-024-01422-z","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10898-024-01422-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-024-01422-z.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/s10898-024-01422-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071995361","display_name":"Mathieu Besan\u00e7on","orcid":"https://orcid.org/0000-0002-6284-3033"},"institutions":[{"id":"https://openalex.org/I195893171","display_name":"Zuse Institute Berlin","ror":"https://ror.org/02eva5865","country_code":"DE","type":"facility","lineage":["https://openalex.org/I195893171"]},{"id":"https://openalex.org/I4210101348","display_name":"Centre Inria de l'Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/00n8d6z93","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210101348"]},{"id":"https://openalex.org/I4210104430","display_name":"Laboratoire d'Informatique de Grenoble","ror":"https://ror.org/01c8rcg82","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210104430","https://openalex.org/I4210159245","https://openalex.org/I899635006","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["DE","FR"],"is_corresponding":true,"raw_author_name":"Mathieu Besan\u00e7on","raw_affiliation_strings":["Universit\u00e9 Grenoble Alpes, Inria, LIG, Grenoble, France","POLARIS - Performance analysis and optimization of LARge Infrastructures and Systems (Laboratoire LIG - B\u00e2timent IMAG - 700 avenue Centrale, CS 40700 - 38058 Grenoble cedex 9 - France)","ZIB - Zuse Institute Berlin (Konrad-Zuse-Zentrum f\u00fcr Informationstechnik Berlin (ZIB Takustra\u00dfe 7 D-14195 Berlin-Dahlem - Germany)","LIG - Laboratoire d'Informatique de Grenoble (UMR 5217 - Laboratoire LIG - B\u00e2timent IMAG - 700 avenue Centrale - Domaine Universitaire de Saint-Martin-d\u2019H\u00e8res \r\nAdresse postale : CS 40700 - 38058 Grenoble cedex 9\r\nT\u00e9l. : 04 57 42 14 00 - France)"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Grenoble Alpes, Inria, LIG, Grenoble, France","institution_ids":["https://openalex.org/I899635006","https://openalex.org/I4210101348","https://openalex.org/I4210104430"]},{"raw_affiliation_string":"POLARIS - Performance analysis and optimization of LARge Infrastructures and Systems (Laboratoire LIG - B\u00e2timent IMAG - 700 avenue Centrale, CS 40700 - 38058 Grenoble cedex 9 - France)","institution_ids":["https://openalex.org/I4210104430"]},{"raw_affiliation_string":"ZIB - Zuse Institute Berlin (Konrad-Zuse-Zentrum f\u00fcr Informationstechnik Berlin (ZIB Takustra\u00dfe 7 D-14195 Berlin-Dahlem - Germany)","institution_ids":["https://openalex.org/I195893171"]},{"raw_affiliation_string":"LIG - Laboratoire d'Informatique de Grenoble (UMR 5217 - Laboratoire LIG - B\u00e2timent IMAG - 700 avenue Centrale - Domaine Universitaire de Saint-Martin-d\u2019H\u00e8res \r\nAdresse postale : CS 40700 - 38058 Grenoble cedex 9\r\nT\u00e9l. : 04 57 42 14 00 - France)","institution_ids":["https://openalex.org/I4210104430"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005540131","display_name":"Miguel F. Anjos","orcid":"https://orcid.org/0000-0002-8258-9116"},"institutions":[{"id":"https://openalex.org/I108192572","display_name":"HEC Montr\u00e9al","ror":"https://ror.org/05ww3wq27","country_code":"CA","type":"education","lineage":["https://openalex.org/I108192572"]},{"id":"https://openalex.org/I3130638677","display_name":"Edinburgh College","ror":"https://ror.org/04vpa6h32","country_code":"GB","type":"education","lineage":["https://openalex.org/I3130638677"]},{"id":"https://openalex.org/I4210133247","display_name":"Group for Research in Decision Analysis","ror":"https://ror.org/02pkvpx84","country_code":"CA","type":"facility","lineage":["https://openalex.org/I108192572","https://openalex.org/I159129438","https://openalex.org/I4210133247","https://openalex.org/I45683168","https://openalex.org/I49663120","https://openalex.org/I5023651"]},{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["CA","GB"],"is_corresponding":false,"raw_author_name":"Miguel F. Anjos","raw_affiliation_strings":["GERAD, 3000, chemin de la C\u00f4te-Sainte-Catherine, Montr\u00e9al, QC, H3T 2A7, Canada","School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK","GERAD - Groupe d\u2019\u00e9tudes et de recherche en analyse des d\u00e9cisions (HEC Montr\u00e9al 3000, chemin de la C\u00f4te-Sainte-Catherine Montr\u00e9al (Qu\u00e9bec) Canada H3T 2A7 - Canada)","Edin. - University of Edinburgh (Old College South Bridge Edinburgh EH8 9YL - United Kingdom)"],"affiliations":[{"raw_affiliation_string":"GERAD, 3000, chemin de la C\u00f4te-Sainte-Catherine, Montr\u00e9al, QC, H3T 2A7, Canada","institution_ids":["https://openalex.org/I108192572","https://openalex.org/I4210133247"]},{"raw_affiliation_string":"School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK","institution_ids":["https://openalex.org/I98677209"]},{"raw_affiliation_string":"GERAD - Groupe d\u2019\u00e9tudes et de recherche en analyse des d\u00e9cisions (HEC Montr\u00e9al 3000, chemin de la C\u00f4te-Sainte-Catherine Montr\u00e9al (Qu\u00e9bec) Canada H3T 2A7 - Canada)","institution_ids":["https://openalex.org/I108192572","https://openalex.org/I4210133247"]},{"raw_affiliation_string":"Edin. - University of Edinburgh (Old College South Bridge Edinburgh EH8 9YL - United Kingdom)","institution_ids":["https://openalex.org/I3130638677","https://openalex.org/I98677209"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021711974","display_name":"Luce Brotcorne","orcid":"https://orcid.org/0000-0002-0906-7709"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I2279609970","display_name":"Universit\u00e9 de Lille","ror":"https://ror.org/02kzqn938","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970"]},{"id":"https://openalex.org/I7454413","display_name":"\u00c9cole Centrale de Lille","ror":"https://ror.org/01x441g73","country_code":"FR","type":"education","lineage":["https://openalex.org/I7454413"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Luce Brotcorne","raw_affiliation_strings":["Centre Inria de l\u2019Universit\u00e9 de Lille, Inria, France and UMR 9189 - CRIStAL, Univ. Lille, CNRS, Centrale Lille, France","INOCS - Integrated Optimization with Complex Structure (France)"],"affiliations":[{"raw_affiliation_string":"Centre Inria de l\u2019Universit\u00e9 de Lille, Inria, France and UMR 9189 - CRIStAL, Univ. Lille, CNRS, Centrale Lille, France","institution_ids":["https://openalex.org/I2279609970","https://openalex.org/I7454413","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"INOCS - Integrated Optimization with Complex Structure (France)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5071995361"],"corresponding_institution_ids":["https://openalex.org/I195893171","https://openalex.org/I4210101348","https://openalex.org/I4210104430","https://openalex.org/I899635006"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2780},"fwci":0.493,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.67485634,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"90","issue":"4","first_page":"813","last_page":"842"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9952999949455261,"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":0.9952999949455261,"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/T10969","display_name":"Water resources management and optimization","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9929999709129333,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bilevel-optimization","display_name":"Bilevel optimization","score":0.9593246579170227},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7983784079551697},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7151892185211182},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.7083932757377625},{"id":"https://openalex.org/keywords/robust-optimization","display_name":"Robust optimization","score":0.6482021808624268},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5561566352844238},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5448378324508667},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.540946364402771},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4864225387573242},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.45399200916290283},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.44183504581451416},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.4369988441467285}],"concepts":[{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.9593246579170227},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7983784079551697},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7151892185211182},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7083932757377625},{"id":"https://openalex.org/C193254401","wikidata":"https://www.wikidata.org/wiki/Q2160088","display_name":"Robust optimization","level":2,"score":0.6482021808624268},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5561566352844238},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5448378324508667},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.540946364402771},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4864225387573242},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.45399200916290283},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.44183504581451416},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.4369988441467285},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10898-024-01422-z","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10898-024-01422-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-024-01422-z.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:publications.polymtl.ca:65063","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401013","display_name":"PolyPublie (\u00c9cole Polytechnique de Montr\u00e9al)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45683168","host_organization_name":"Polytechnique Montr\u00e9al","host_organization_lineage":["https://openalex.org/I45683168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:HAL:hal-04792534v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04792534","pdf_url":"https://hal.science/hal-04792534/document","source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Journal of Global Optimization, 2024, 90 (4), pp.813-842. ⟨10.1007/s10898-024-01422-z⟩","raw_type":"Journal articles"},{"id":"pmh:oai:RePEc:spr:jglopt:v:90:y:2024:i:4:d:10.1007_s10898-024-01422-z","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10898-024-01422-z","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/s10898-024-01422-z","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10898-024-01422-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-024-01422-z.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":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4401134013.pdf"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W49793390","https://openalex.org/W141031297","https://openalex.org/W188934197","https://openalex.org/W1588628884","https://openalex.org/W1632601927","https://openalex.org/W1741718720","https://openalex.org/W1918816242","https://openalex.org/W1965897919","https://openalex.org/W1970933528","https://openalex.org/W1974549991","https://openalex.org/W1977649329","https://openalex.org/W2022954527","https://openalex.org/W2037678919","https://openalex.org/W2039551591","https://openalex.org/W2042838878","https://openalex.org/W2043339930","https://openalex.org/W2066111511","https://openalex.org/W2102529199","https://openalex.org/W2120575449","https://openalex.org/W2140496876","https://openalex.org/W2163969905","https://openalex.org/W2164945937","https://openalex.org/W2168092276","https://openalex.org/W2234594789","https://openalex.org/W2499145065","https://openalex.org/W2560324934","https://openalex.org/W2745660793","https://openalex.org/W2747319311","https://openalex.org/W2765224644","https://openalex.org/W2888211270","https://openalex.org/W2950961269","https://openalex.org/W2963920200","https://openalex.org/W2994418322","https://openalex.org/W3006959147","https://openalex.org/W3034772278","https://openalex.org/W3038643818","https://openalex.org/W3038794973","https://openalex.org/W3096847493","https://openalex.org/W3105558219","https://openalex.org/W3107118572","https://openalex.org/W3161399930","https://openalex.org/W3176021395","https://openalex.org/W3194404705","https://openalex.org/W3209928754","https://openalex.org/W4205717391","https://openalex.org/W4250589301","https://openalex.org/W4318942333","https://openalex.org/W4393527376","https://openalex.org/W4401730499","https://openalex.org/W6759803958","https://openalex.org/W6912109035","https://openalex.org/W6949805966"],"related_works":["https://openalex.org/W3161399930","https://openalex.org/W2890257643","https://openalex.org/W1495503294","https://openalex.org/W3149055374","https://openalex.org/W2161149697","https://openalex.org/W2216231335","https://openalex.org/W2884337142","https://openalex.org/W2340378315","https://openalex.org/W255338418","https://openalex.org/W2602322400"],"abstract_inverted_index":{"Abstract":[0],"Bilevel":[1],"optimization":[2,15,62],"problems":[3],"embed":[4],"the":[5,19,28,36,40,49,71,77,80,88,96,102],"optimality":[6],"of":[7,13,21,51,59,90,98],"a":[8,11],"subproblem":[9],"as":[10],"constraint":[12],"another":[14],"problem.":[16],"We":[17],"introduce":[18],"concept":[20],"near-optimality":[22],"robustness":[23],"for":[24,48,55],"bilevel":[25,61,83],"optimization,":[26],"protecting":[27],"upper-level":[29],"solution":[30,38,66,103],"feasibility":[31],"from":[32,35,79],"limited":[33],"deviations":[34],"optimal":[37],"at":[39],"lower":[41,72],"level.":[42],"General":[43],"properties":[44],"and":[45,82,92,95],"necessary":[46],"conditions":[47],"existence":[50],"solutions":[52],"are":[53],"derived":[54],"near-optimal":[56],"robust":[57,81],"versions":[58],"general":[60],"problems.":[63],"A":[64],"duality-based":[65],"method":[67],"is":[68,74],"defined":[69],"when":[70],"level":[73],"convex,":[75],"leveraging":[76],"methodology":[78],"literature.":[84],"Numerical":[85],"results":[86],"assess":[87],"efficiency":[89],"exact":[91],"heuristic":[93],"methods":[94],"impact":[97],"valid":[99],"inequalities":[100],"on":[101],"time.":[104]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-27T14:29:43.386196","created_date":"2025-10-10T00:00:00"}