{"id":"https://openalex.org/W4393144506","doi":"https://doi.org/10.1137/22m1543367","title":"Consensus-Based Optimization for Saddle Point Problems","display_name":"Consensus-Based Optimization for Saddle Point Problems","publication_year":2024,"publication_date":"2024-03-25","ids":{"openalex":"https://openalex.org/W4393144506","doi":"https://doi.org/10.1137/22m1543367"},"language":"en","primary_location":{"id":"doi:10.1137/22m1543367","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1543367","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","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/A5011633768","display_name":"Hui Huang","orcid":"https://orcid.org/0000-0002-4171-0530"},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Hui Huang","raw_affiliation_strings":["Department of Mathematics and Scientific Computing, University of Graz, 8010 Graz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Scientific Computing, University of Graz, 8010 Graz, Austria","institution_ids":["https://openalex.org/I15766117"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028944622","display_name":"Jinniao Qiu","orcid":null},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Jinniao Qiu","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Calgary, T2N 1N4 Calgary, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Calgary, T2N 1N4 Calgary, Canada","institution_ids":["https://openalex.org/I168635309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088292594","display_name":"Konstantin Riedl","orcid":"https://orcid.org/0000-0002-2206-4334"},"institutions":[{"id":"https://openalex.org/I292141241","display_name":"Munich School of Philosophy","ror":"https://ror.org/02kqy4228","country_code":"DE","type":"education","lineage":["https://openalex.org/I292141241"]},{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Konstantin Riedl","raw_affiliation_strings":["Department of Mathematics, School of Computation, Information and Technology, Technical University of Munich, 80333 Munich, Germany","Munich Center for Machine Learning, 80593 Munich, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Computation, Information and Technology, Technical University of Munich, 80333 Munich, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Munich Center for Machine Learning, 80593 Munich, Germany","institution_ids":["https://openalex.org/I292141241"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.5227,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.98554368,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"62","issue":"2","first_page":"1093","last_page":"1121"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983999729156494,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983999729156494,"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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9919000267982483,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9872000217437744,"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/mathematics","display_name":"Mathematics","score":0.7875652313232422},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.7424277067184448},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5740385055541992},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.467805415391922},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.46728262305259705},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.45117536187171936},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.40714210271835327},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35897213220596313},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1318511664867401}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7875652313232422},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.7424277067184448},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5740385055541992},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.467805415391922},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.46728262305259705},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.45117536187171936},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.40714210271835327},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35897213220596313},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1318511664867401},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1543367","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1543367","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310984","display_name":"Pacific Institute for the Mathematical Sciences","ror":"https://ror.org/04w49dw51"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W609447776","https://openalex.org/W1521946947","https://openalex.org/W1595431397","https://openalex.org/W1985077192","https://openalex.org/W2003083760","https://openalex.org/W2039996159","https://openalex.org/W2067050450","https://openalex.org/W2075567596","https://openalex.org/W2079135578","https://openalex.org/W2110667918","https://openalex.org/W2119895058","https://openalex.org/W2145137020","https://openalex.org/W2340142742","https://openalex.org/W2569616450","https://openalex.org/W2963356890","https://openalex.org/W3021435406","https://openalex.org/W3035625450","https://openalex.org/W3044387630","https://openalex.org/W3083025901","https://openalex.org/W3096831136","https://openalex.org/W3105504331","https://openalex.org/W3111474949","https://openalex.org/W3125335477","https://openalex.org/W3148774867","https://openalex.org/W3164389725","https://openalex.org/W3210826202","https://openalex.org/W3212328538","https://openalex.org/W3216340729","https://openalex.org/W4205841652","https://openalex.org/W4206742934","https://openalex.org/W4238187298","https://openalex.org/W4378878907","https://openalex.org/W4387820169"],"related_works":["https://openalex.org/W4236459141","https://openalex.org/W4205304778","https://openalex.org/W2020252434","https://openalex.org/W73248859","https://openalex.org/W2584253892","https://openalex.org/W2350324449","https://openalex.org/W1572705989","https://openalex.org/W119381072","https://openalex.org/W2034033896","https://openalex.org/W2087062149"],"abstract_inverted_index":{".In":[0],"this":[1],"paper,":[2],"we":[3],"propose":[4],"consensus-based":[5],"optimization":[6,17],"for":[7,115],"saddle":[8],"point":[9,121],"problems":[10],"(CBO-SP),":[11],"a":[12,43,52,65,72],"novel":[13],"multi-particle":[14],"metaheuristic":[15],"derivative-free":[16],"method":[18,33,81],"capable":[19],"of":[20,29,37,118],"provably":[21],"finding":[22],"global":[23],"Nash":[24],"equilibria.":[25],"Following":[26],"the":[27,32,49,55,75,80,98,101,116,119],"idea":[28],"swarm":[30],"intelligence,":[31],"employs":[34],"two":[35,59],"groups":[36,60],"interacting":[38],"particles,":[39],"one":[40,46],"which":[41,78,104],"performs":[42,51],"minimization":[44],"over":[45,54],"variable":[47],"while":[48],"other":[50,56],"maximization":[53],"variable.":[57],"The":[58],"constantly":[61],"exchange":[62],"information":[63],"through":[64],"suitably":[66],"weighted":[67],"average.":[68],"This":[69],"paradigm":[70],"permits":[71],"passage":[73],"to":[74,83,89],"mean-field":[76],"limit,":[77],"makes":[79],"amenable":[82],"theoretical":[84],"analysis,":[85],"and":[86,100],"it":[87],"allows":[88],"obtain":[90],"rigorous":[91],"convergence":[92],"guarantees":[93],"under":[94],"reasonable":[95],"assumptions":[96],"about":[97],"initialization":[99],"objective":[102],"function,":[103],"most":[105],"notably":[106],"include":[107],"nonconvex-nonconcave":[108],"objectives.":[109],"We":[110],"further":[111],"provide":[112],"numerical":[113],"evidence":[114],"success":[117],"algorithm.Keywordssaddle":[120],"problemsNash":[122],"equilibria":[123],"nonconvex-nonconcavederivative-free":[124],"optimizationmetaheuristicsconsensus-based":[125],"optimizationFokker\u2013Planck":[126],"equationsMSC":[127],"codes90C4765C3565K0590C5635Q9035Q83":[128]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
