{"id":"https://openalex.org/W7128813084","doi":"https://doi.org/10.48550/arxiv.2602.11835","title":"Global Convergence to Nash Equilibrium in Nonconvex General-Sum Games under the $n$-Sided PL Condition","display_name":"Global Convergence to Nash Equilibrium in Nonconvex General-Sum Games under the $n$-Sided PL Condition","publication_year":2026,"publication_date":"2026-02-12","ids":{"openalex":"https://openalex.org/W7128813084","doi":"https://doi.org/10.48550/arxiv.2602.11835"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.11835","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5125893051","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":"last","author":{"id":"https://openalex.org/A5029215185","display_name":"Jalal Etesami","orcid":"https://orcid.org/0000-0002-7404-5952"},"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":0.31209999322891235,"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":0.31209999322891235,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.24940000474452972,"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"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.1704999953508377,"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/convergence","display_name":"Convergence (economics)","score":0.7166000008583069},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.6898000240325928},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4968999922275543},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.45350000262260437},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.42890000343322754},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.39739999175071716}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7166000008583069},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.6898000240325928},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5752000212669373},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5256999731063843},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4968999922275543},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.45350000262260437},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.42890000343322754},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.39739999175071716},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.37059998512268066},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34450000524520874},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.33379998803138733},{"id":"https://openalex.org/C22349654","wikidata":"https://www.wikidata.org/wiki/Q2039354","display_name":"Risk dominance","level":5,"score":0.33230000734329224},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.3176000118255615},{"id":"https://openalex.org/C157553263","wikidata":"https://www.wikidata.org/wiki/Q5168004","display_name":"Coordinate descent","level":2,"score":0.31130000948905945},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3102000057697296},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.2653999924659729}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.11835","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.11835","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.11835","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.11835","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,52],"consider":[1],"the":[2,23,42,59,65,75,92,107,138,141],"problem":[3],"of":[4,26,56,77,85,94,124,140],"finding":[5],"a":[6,11,54],"Nash":[7],"equilibrium":[8],"(NE)":[9],"in":[10],"general-sum":[12],"game,":[13],"where":[14,106],"player":[15,27],"$i$'s":[16],"objective":[17],"is":[18,31],"$f_i(x)=f_i(x_1,...,x_n)$,":[19],"with":[20],"$x_j\\in\\mathbb{R}^{d_j}$":[21],"denoting":[22],"strategy":[24],"variables":[25],"$j$.":[28],"Our":[29],"focus":[30],"on":[32],"investigating":[33],"first-order":[34],"gradient-based":[35],"algorithms":[36,143],"and":[37,74,130],"their":[38,132],"variations,":[39],"such":[40,118],"as":[41],"block":[43],"coordinate":[44],"descent":[45,97,110],"(BCD)":[46],"algorithm,":[47],"for":[48],"tackling":[49],"this":[50],"problem.":[51],"introduce":[53],"set":[55],"conditions,":[57],"called":[58],"$n$-sided":[60],"PL":[61],"condition,":[62,80],"which":[63],"extends":[64],"well-established":[66],"gradient":[67,96,109],"dominance":[68],"condition":[69,73],"a.k.a":[70],"Polyak-\u0141ojasiewicz":[71],"(PL)":[72],"concept":[76],"multi-convexity.":[78],"This":[79],"satisfied":[81],"by":[82],"various":[83,95],"classes":[84],"non-convex":[86],"functions,":[87],"allows":[88],"us":[89],"to":[90,113,115],"analyze":[91,131],"convergence":[93,133],"(GD)":[98],"algorithms.":[99],"Moreover,":[100],"our":[101],"study":[102],"delves":[103],"into":[104],"scenarios":[105],"standard":[108],"methods":[111],"fail":[112],"converge":[114,127],"NE.":[116],"In":[117],"cases,":[119],"we":[120,136],"propose":[121],"adapted":[122],"variants":[123],"GD":[125],"that":[126],"towards":[128],"NE":[129],"rates.":[134],"Finally,":[135],"evaluate":[137],"performance":[139],"proposed":[142],"through":[144],"several":[145],"experiments.":[146]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-02-14T00:00:00"}