{"id":"https://openalex.org/W7161849513","doi":"https://doi.org/10.48550/arxiv.2605.19667","title":"Convergence of Consensus-Based Particle Methods for Nonconvex Bi-Level Optimization","display_name":"Convergence of Consensus-Based Particle Methods for Nonconvex Bi-Level Optimization","publication_year":2026,"publication_date":"2026-05-19","ids":{"openalex":"https://openalex.org/W7161849513","doi":"https://doi.org/10.48550/arxiv.2605.19667"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.19667","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.19667","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.19667","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136563143","display_name":"Yutong Chao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chao, Yutong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136534173","display_name":"Xudong Sun","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sun, Xudong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136542572","display_name":"Konstantin Riedl","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Riedl, Konstantin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043216529","display_name":"Majid Khadiv","orcid":"https://orcid.org/0000-0001-9889-6543"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Khadiv, Majid","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5136512438","display_name":"Jalal Etesami","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Etesami, Jalal","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.621399998664856,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.621399998664856,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.11479999870061874,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.06970000267028809,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/convergence","display_name":"Convergence (economics)","score":0.6438999772071838},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47440001368522644},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.4740000069141388},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4537000060081482},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4390000104904175},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4368000030517578},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.4221999943256378},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4131999909877777}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6784999966621399},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6438999772071838},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6014999747276306},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5781000256538391},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47440001368522644},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.4740000069141388},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4537000060081482},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4390000104904175},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4368000030517578},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.4221999943256378},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4131999909877777},{"id":"https://openalex.org/C118671147","wikidata":"https://www.wikidata.org/wiki/Q578714","display_name":"Quantile","level":2,"score":0.3917999863624573},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.38679999113082886},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3637999892234802},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.29260000586509705},{"id":"https://openalex.org/C164752517","wikidata":"https://www.wikidata.org/wiki/Q5570875","display_name":"Global optimization","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C177067428","wikidata":"https://www.wikidata.org/wiki/Q17013331","display_name":"Feasible region","level":2,"score":0.2759999930858612},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.275299996137619},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.2574999928474426},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2531000077724457}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.19667","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.19667","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.19667","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.19667","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"score":0.7736979722976685,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0,66],"this":[1],"paper,":[2],"we":[3,79],"study":[4],"a":[5,29,48,109],"consensus-based":[6],"optimization":[7],"method":[8],"for":[9,56],"nonconvex":[10],"bi-level":[11,94],"optimization,":[12],"where":[13],"the":[14,23,58,82,92,103,119],"objective":[15],"is":[16,35],"to":[17,102],"minimize":[18],"an":[19,97],"upper-level":[20],"function":[21],"over":[22],"set":[24],"of":[25,28,91],"global":[26],"minimizers":[27],"lower-level":[30],"problem.":[31],"The":[32],"proposed":[33],"approach":[34],"derivative-free,":[36],"and":[37,62,77,113],"constructs":[38],"its":[39,63],"consensus":[40],"point":[41],"via":[42],"smooth":[43,72],"quantile":[44,73],"selection":[45],"combined":[46],"with":[47,96],"Gibbs-type":[49],"Laplace":[50],"approximation.":[51,65],"We":[52],"establish":[53],"convergence":[54],"guarantees":[55],"both":[57],"associated":[59],"\\textit{mean-field}":[60],"dynamics":[61],"\\textit{finite-particle}":[64],"particular,":[67],"under":[68],"suitable":[69],"assumptions":[70],"on":[71,108],"localization,":[74],"error":[75],"bounds,":[76],"stability,":[78],"show":[80],"that":[81],"mean-field":[83],"law":[84],"reaches":[85],"any":[86],"arbitrary":[87],"prescribed":[88],"Wasserstein":[89],"neighborhood":[90],"target":[93],"solution":[95],"explicit":[98],"exponential":[99],"rate":[100],"up":[101],"hitting":[104],"time.":[105],"Numerical":[106],"experiments":[107],"two-dimensional":[110],"constrained":[111],"problem":[112],"neural":[114],"network":[115],"training":[116],"further":[117],"support":[118],"theoretical":[120],"results.":[121]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-21T00:00:00"}
