{"id":"https://openalex.org/W3160248732","doi":"https://doi.org/10.1007/s00186-024-00852-5","title":"Trilevel and multilevel optimization using\u00a0monotone\u00a0operator\u00a0theory","display_name":"Trilevel and multilevel optimization using\u00a0monotone\u00a0operator\u00a0theory","publication_year":2024,"publication_date":"2024-02-28","ids":{"openalex":"https://openalex.org/W3160248732","doi":"https://doi.org/10.1007/s00186-024-00852-5","mag":"3160248732"},"language":"en","primary_location":{"id":"doi:10.1007/s00186-024-00852-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00186-024-00852-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00186-024-00852-5.pdf","source":{"id":"https://openalex.org/S126160977","display_name":"Mathematical Methods of Operations Research","issn_l":"1432-2994","issn":["1432-2994","1432-5217"],"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":"Mathematical Methods of Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00186-024-00852-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090249140","display_name":"Allahkaram Shafiei","orcid":"https://orcid.org/0000-0002-1415-2166"},"institutions":[{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Allahkaram Shafiei","raw_affiliation_strings":["Department of Computer Science, Czech Technical University, Karlovo Namesti 13, 121 35, Prague 2, Czech Republic"],"raw_orcid":"https://orcid.org/0000-0002-1415-2166","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Czech Technical University, Karlovo Namesti 13, 121 35, Prague 2, Czech Republic","institution_ids":["https://openalex.org/I44504214"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066151990","display_name":"Vyacheslav Kungurtsev","orcid":"https://orcid.org/0000-0003-2229-8824"},"institutions":[{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Vyacheslav Kungurtsev","raw_affiliation_strings":["Department of Computer Science, Czech Technical University, Karlovo Namesti 13, 121 35, Prague 2, Czech Republic"],"raw_orcid":"https://orcid.org/0000-0003-2229-8824","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Czech Technical University, Karlovo Namesti 13, 121 35, Prague 2, Czech Republic","institution_ids":["https://openalex.org/I44504214"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003656133","display_name":"Jakub Mare\u010dek","orcid":"https://orcid.org/0000-0003-0839-0691"},"institutions":[{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Jakub Marecek","raw_affiliation_strings":["Department of Computer Science, Czech Technical University, Karlovo Namesti 13, 121 35, Prague 2, Czech Republic"],"raw_orcid":"https://orcid.org/0000-0003-0839-0691","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Czech Technical University, Karlovo Namesti 13, 121 35, Prague 2, Czech Republic","institution_ids":["https://openalex.org/I44504214"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5003656133"],"corresponding_institution_ids":["https://openalex.org/I44504214"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.5127,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.62182101,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"99","issue":"1-2","first_page":"77","last_page":"114"},"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":0.9987000226974487,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.6551923155784607},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6421263813972473},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6378015875816345},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5375264883041382},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.532227098941803},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5216496586799622},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.513748288154602},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4547719955444336},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4346904754638672}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6551923155784607},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6421263813972473},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6378015875816345},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5375264883041382},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.532227098941803},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5216496586799622},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.513748288154602},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4547719955444336},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4346904754638672},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00186-024-00852-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00186-024-00852-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00186-024-00852-5.pdf","source":{"id":"https://openalex.org/S126160977","display_name":"Mathematical Methods of Operations Research","issn_l":"1432-2994","issn":["1432-2994","1432-5217"],"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":"Mathematical Methods of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2105.09407","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2105.09407","pdf_url":"https://arxiv.org/pdf/2105.09407","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"pmh:oai:HAL:hal-04925417v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04925417","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Methods of Operations Research, 2024, 99 (1-2), pp.77-114. &#x27E8;10.1007/s00186-024-00852-5&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:RePEc:spr:mathme:v:99:y:2024:i:1:d:10.1007_s00186-024-00852-5","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s00186-024-00852-5","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/s00186-024-00852-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00186-024-00852-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00186-024-00852-5.pdf","source":{"id":"https://openalex.org/S126160977","display_name":"Mathematical Methods of Operations Research","issn_l":"1432-2994","issn":["1432-2994","1432-5217"],"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":"Mathematical Methods of Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1062818326","display_name":"Human-Compatible Artificial Intelligence with Guarantees","funder_award_id":"101070568","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G12500569","display_name":null,"funder_award_id":"CZ.02.1.01/0.0","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G3622461675","display_name":null,"funder_award_id":"CZ.02.1.01","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4131035492","display_name":null,"funder_award_id":"CZ.02.1.01","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G6304920596","display_name":null,"funder_award_id":"101070568","funder_id":"https://openalex.org/F4320334322","funder_display_name":"HORIZON EUROPE Framework Programme"},{"id":"https://openalex.org/G7722404536","display_name":null,"funder_award_id":"CZ.02.1.01/0.0/0.0/16_019/0000765","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8083513858","display_name":null,"funder_award_id":"16_019/0000765","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G818148623","display_name":null,"funder_award_id":"TN02000025","funder_id":"https://openalex.org/F4320321623","funder_display_name":"Technologick\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G8277801703","display_name":null,"funder_award_id":"22-15524\u00a0S","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"}],"funders":[{"id":"https://openalex.org/F4320309972","display_name":"\u010cesk\u00e9 Vysok\u00e9 U\u010den\u00ed Technick\u00e9 v Praze","ror":"https://ror.org/03kqpb082"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"},{"id":"https://openalex.org/F4320321623","display_name":"Technologick\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/04v0fk911"},{"id":"https://openalex.org/F4320322832","display_name":"University of Tokyo","ror":"https://ror.org/057zh3y96"},{"id":"https://openalex.org/F4320334322","display_name":"HORIZON EUROPE Framework Programme","ror":null},{"id":"https://openalex.org/F4320335125","display_name":"RIKEN","ror":"https://ror.org/01sjwvz98"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3160248732.pdf"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W205960364","https://openalex.org/W1481730903","https://openalex.org/W1546168022","https://openalex.org/W1853237406","https://openalex.org/W1979084875","https://openalex.org/W2021361347","https://openalex.org/W2021902942","https://openalex.org/W2031264011","https://openalex.org/W2033511209","https://openalex.org/W2033943991","https://openalex.org/W2045014872","https://openalex.org/W2051076175","https://openalex.org/W2063909906","https://openalex.org/W2064997474","https://openalex.org/W2069577676","https://openalex.org/W2085440994","https://openalex.org/W2085771669","https://openalex.org/W2100556411","https://openalex.org/W2124541940","https://openalex.org/W2129704204","https://openalex.org/W2134230680","https://openalex.org/W2134851358","https://openalex.org/W2288883172","https://openalex.org/W2606904667","https://openalex.org/W2748976149","https://openalex.org/W2951117356","https://openalex.org/W2962704982","https://openalex.org/W3040576633","https://openalex.org/W3103639684","https://openalex.org/W3141595720","https://openalex.org/W4229650096","https://openalex.org/W4251616545","https://openalex.org/W4303084602"],"related_works":["https://openalex.org/W2784494936","https://openalex.org/W3153752017","https://openalex.org/W4387635768","https://openalex.org/W2756132392","https://openalex.org/W2985979428","https://openalex.org/W3035814349","https://openalex.org/W2510140549","https://openalex.org/W2187449906","https://openalex.org/W4285101096","https://openalex.org/W4382725876"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"consider":[2,35],"rather":[3],"a":[4,12,31,36,50,53,56,68],"general":[5],"class":[6],"of":[7,23,25,43,49,52,78,83],"multi-level":[8],"optimization":[9,28,38],"problems,":[10],"where":[11,40],"convex":[13,27],"objective":[14,42],"function":[15],"is":[16],"to":[17,21],"be":[18],"minimized":[19],"subject":[20],"constraints":[22],"optimality":[24],"nested":[26],"problems.":[29],"As":[30],"special":[32],"case,":[33],"we":[34,66],"trilevel":[37],"problem,":[39],"the":[41,44],"two":[45],"lower":[46],"layers":[47],"consists":[48],"sum":[51],"smooth":[54],"and":[55,63,72,76],"non-smooth":[57],"term.":[58],"Based":[59],"on":[60],"fixed-point":[61],"theory":[62],"related":[64],"arguments,":[65],"present":[67],"natural":[69],"first-order":[70],"algorithm":[71],"analyze":[73],"its":[74],"convergence":[75,79],"rates":[77],"in":[80],"several":[81],"regimes":[82],"parameters.":[84]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
