{"id":"https://openalex.org/W7214092953","doi":"https://doi.org/10.48550/arxiv.2609.25752","title":"Efficient Parameter-Free First-Order Methods for Nonsmooth Composite Minimax Optimization","display_name":"Efficient Parameter-Free First-Order Methods for Nonsmooth Composite Minimax Optimization","publication_year":2026,"publication_date":"2026-09-22","ids":{"openalex":"https://openalex.org/W7214092953","doi":"https://doi.org/10.48550/arxiv.2609.25752"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.25752","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25752","pdf_url":"https://arxiv.org/pdf/2609.25752","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.25752","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152551219","display_name":"Shaozhe Ke","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Ke, Shaozhe","raw_affiliation_strings":["Department of Industrial Engineering and Decision Analytics , Hong Kong University of Science and Technology , Hong Kong , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Decision Analytics , Hong Kong University of Science and Technology , Hong Kong , China","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050252539","display_name":"Sanyou Mei","orcid":"https://orcid.org/0009-0001-9028-7847","observed_orcids":["https://orcid.org/0009-0001-9028-7847"]},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Mei, Sanyou","raw_affiliation_strings":["Department of Industrial Engineering and Decision Analytics , Hong Kong University of Science and Technology , Hong Kong , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Decision Analytics , Hong Kong University of Science and Technology , Hong Kong , China","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004297494","display_name":"Jiheng Zhang","orcid":"https://orcid.org/0000-0003-3025-1495","observed_orcids":["https://orcid.org/0000-0003-3025-1495"]},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Zhang, Jiheng","raw_affiliation_strings":["Department of Industrial Engineering and Decision Analytics , Hong Kong University of Science and Technology , Hong Kong , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Decision Analytics , Hong Kong University of Science and Technology , Hong Kong , China","institution_ids":["https://openalex.org/I200769079"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I200769079"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":0.5692999958992004,"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":0.5692999958992004,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.3546999990940094,"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":0.05559999868273735,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/min-max-optimization","display_name":"minimax optimization","score":0.8019999861717224},{"id":"https://openalex.org/keywords/nonsmooth-optimization","display_name":"nonsmooth optimization","score":0.9079999923706055},{"id":"https://openalex.org/keywords/composite-optimization","display_name":"composite optimization","score":0.8519999980926514},{"id":"https://openalex.org/keywords/first-order-methods","display_name":"first-order methods","score":0.875},{"id":"https://openalex.org/keywords/parameter-free-method","display_name":"parameter-free method","score":0.847000002861023},{"id":"https://openalex.org/keywords/proximal-point-algorithm","display_name":"proximal point algorithm","score":0.996999979019165},{"id":"https://openalex.org/keywords/operation-complexity","display_name":"operation complexity","score":0.7789999842643738}],"concepts":[{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.7545999884605408},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.661899983882904},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5831999778747559},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5566999912261963},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5422999858856201},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5270000100135803},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.519599974155426},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5063999891281128},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.39719998836517334},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3767000138759613},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3747999966144562},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3564999997615814},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33500000834465027},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.3280999958515167},{"id":"https://openalex.org/C2780861221","wikidata":"https://www.wikidata.org/wiki/Q913849","display_name":"Minimax theorem","level":3,"score":0.3228999972343445},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.31470000743865967},{"id":"https://openalex.org/C104779481","wikidata":"https://www.wikidata.org/wiki/Q50707","display_name":"Composite number","level":2,"score":0.29840001463890076},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.25752","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25752","pdf_url":"https://arxiv.org/pdf/2609.25752","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.25752","doi":"https://doi.org/10.48550/arxiv.2609.25752","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.25752","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.25752","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25752","pdf_url":"https://arxiv.org/pdf/2609.25752","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214092953.pdf","grobid_xml":"https://content.openalex.org/works/W7214092953.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W3023174339","https://openalex.org/W3175461813","https://openalex.org/W4386291915","https://openalex.org/W4387804153","https://openalex.org/W4401306562","https://openalex.org/W6903753222","https://openalex.org/W7129486269","https://openalex.org/W7213350592"],"related_works":["https://openalex.org/W4402242253","https://openalex.org/W2954249541","https://openalex.org/W7027361433","https://openalex.org/W4384652316","https://openalex.org/W3209048521","https://openalex.org/W3096194929","https://openalex.org/W4401306562","https://openalex.org/W2001732520","https://openalex.org/W4417068666","https://openalex.org/W4391654279"],"abstract_inverted_index":{"In":[0],"this":[1,57],"paper":[2],"we":[3,62],"propose":[4,63],"first-order":[5],"methods":[6,118],"for":[7,32,68,101],"a":[8,60,64],"class":[9],"of":[10,83,112],"nonsmooth":[11],"composite":[12],"strongly":[13,33],"convex--strongly":[14,34],"concave":[15,35],"and":[16,27,47,105],"nonconvex--concave":[17,69],"minimax":[18],"optimization.":[19],"We":[20,96],"first":[21],"develop":[22,98],"an":[23,28,76,80],"inexact":[24],"proximal":[25,65],"method":[26,31,58,67],"accumulative":[29],"regularizated":[30],"problems.":[36,70],"The":[37],"latter":[38],"achieves":[39],"the":[40,44,49,53,87,93,107],"optimal":[41],"dependence":[42],"on":[43],"curvature":[45,51],"parameters":[46],"places":[48],"smaller":[50],"inside":[52],"accuracy":[54],"logarithm.":[55],"Using":[56],"as":[59],"subsolver,":[61],"point":[66,78],"Under":[71],"suitable":[72],"assumptions,":[73],"it":[74],"finds":[75],"$\u03b5$-stationary":[77],"with":[79,121],"operation":[81],"complexity":[82,109],"$O(\u03b5^{-5/2})$,":[84],"which":[85],"improves":[86],"best-known":[88],"$O(\u03b5^{-5/2}\\log(1/\u03b5))$":[89],"bounds":[90],"by":[91],"removing":[92],"logarithmic":[94],"factor.":[95],"further":[97],"parameter-free":[99],"variants":[100],"both":[102],"problem":[103,114],"classes,":[104],"achieve":[106],"same":[108],"without":[110],"knowledge":[111],"any":[113],"constants.":[115],"All":[116],"proposed":[117],"are":[119],"equipped":[120],"verifiable":[122],"termination":[123],"criteria.":[124]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-24T00:00:00"}
