{"id":"https://openalex.org/W7214033371","doi":"https://doi.org/10.48550/arxiv.2609.23837","title":"The Exponential Price of Determinism in Nonsmooth Nonconvex Optimization","display_name":"The Exponential Price of Determinism in Nonsmooth Nonconvex Optimization","publication_year":2026,"publication_date":"2026-09-20","ids":{"openalex":"https://openalex.org/W7214033371","doi":"https://doi.org/10.48550/arxiv.2609.23837"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.23837","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23837","pdf_url":"https://arxiv.org/pdf/2609.23837","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/2609.23837","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064469637","display_name":"Guy Kornowski","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kornowski, Guy","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5064469637"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":5,"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":0.9125999808311462,"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":0.9125999808311462,"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":0.0568000003695488,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.01889999955892563,"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/nonsmooth-nonconvex-optimization","display_name":"nonsmooth nonconvex optimization","score":0.9860000014305115},{"id":"https://openalex.org/keywords/deterministic-algorithms","display_name":"deterministic algorithms","score":0.4970000088214874},{"id":"https://openalex.org/keywords/randomized-algorithms","display_name":"randomized algorithms","score":0.781000018119812},{"id":"https://openalex.org/keywords/oracle-complexity","display_name":"oracle complexity","score":0.6859999895095825},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.8700000047683716},{"id":"https://openalex.org/keywords/lipschitz-functions","display_name":"Lipschitz functions","score":0.828000009059906},{"id":"https://openalex.org/keywords/descent-direction","display_name":"descent direction","score":0.546999990940094}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.765999972820282},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5623999834060669},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.5246999859809875},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.47530001401901245},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4675999879837036},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4593999981880188},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4291999936103821},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4016000032424927},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.39329999685287476},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.3846000134944916},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.366100013256073},{"id":"https://openalex.org/C13533509","wikidata":"https://www.wikidata.org/wiki/Q1064349","display_name":"Deterministic algorithm","level":2,"score":0.3644999861717224},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3330000042915344},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.32100000977516174},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.3179999887943268},{"id":"https://openalex.org/C2778775528","wikidata":"https://www.wikidata.org/wiki/Q5135432","display_name":"Closing (real estate)","level":2,"score":0.30559998750686646},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.30239999294281006},{"id":"https://openalex.org/C71017364","wikidata":"https://www.wikidata.org/wiki/Q5421532","display_name":"Exponential time hypothesis","level":3,"score":0.30169999599456787},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.2881999909877777},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.28049999475479126},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.2768999934196472},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.26809999346733093},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.2648000121116638},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.257999986410141}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.23837","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23837","pdf_url":"https://arxiv.org/pdf/2609.23837","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.2609.23837","doi":"https://doi.org/10.48550/arxiv.2609.23837","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.23837","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:2609.23837","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23837","pdf_url":"https://arxiv.org/pdf/2609.23837","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214033371.pdf","grobid_xml":"https://content.openalex.org/works/W7214033371.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W7155539384","https://openalex.org/W7171525360","https://openalex.org/W7204546023"],"related_works":["https://openalex.org/W4297434938","https://openalex.org/W4321277027","https://openalex.org/W4390637589","https://openalex.org/W7213523973","https://openalex.org/W4383993447","https://openalex.org/W4389137367","https://openalex.org/W4297899866","https://openalex.org/W4403702737","https://openalex.org/W7172487772","https://openalex.org/W7214957700"],"abstract_inverted_index":{"We":[0,77,116],"study":[1],"the":[2,49,69,94,98],"complexity":[3,31,42,73],"of":[4,9,87,123],"finding":[5,130],"$(\u03b4,\u03b5)$-Goldstein":[6],"stationary":[7],"points":[8],"nonsmooth":[10,146],"nonconvex":[11,147],"Lipschitz":[12],"functions.":[13],"By":[14],"now,":[15],"it":[16],"is":[17],"known":[18,100],"that":[19],"randomized":[20],"first-order":[21],"algorithms":[22,38,65],"can":[23,66],"solve":[24,68],"this":[25,79,124],"task":[26],"with":[27,48,71],"a":[28,84,131],"dimension-free":[29],"oracle":[30,72],"[Zhang":[32],"et":[33,53,113],"al.,":[34,54],"2020],":[35],"whereas":[36],"deterministic":[37,64,91,135],"cannot,":[39],"as":[40],"their":[41],"must":[43],"scale":[44],"at":[45],"least":[46],"linearly":[47],"dimension":[50],"$d$":[51],"[Jordan":[52],"2023,":[55],"Tian":[56],"and":[57,102,105,121,134],"So,":[58],"2024].":[59],"This":[60],"leaves":[61],"open":[62,108],"whether":[63],"nevertheless":[67],"problem":[70,109],"polynomial":[74],"in":[75,145],"$d$.":[76],"answer":[78],"question":[80],"negatively":[81],"by":[82,111,150],"proving":[83],"lower":[85,101],"bound":[86],"order":[88],"$(1/\u03b5)^{\u03a9(d)}$":[89],"for":[90],"algorithm,":[92],"closing":[93],"exponential":[95,142],"gap":[96],"between":[97],"previously":[99],"upper":[103],"bounds":[104],"resolving":[106],"an":[107,141],"posed":[110],"Jordan":[112],"al.":[114],"[2023].":[115],"further":[117],"discuss":[118],"several":[119],"extensions":[120],"implications":[122],"result":[125],"to":[126],"weaker":[127],"stationarity":[128],"notions,":[129],"descent":[132],"direction":[133],"smoothing.":[136],"Overall,":[137],"our":[138],"results":[139],"establish":[140],"computational":[143],"advantage":[144],"optimization":[148],"offered":[149],"randomization.":[151]},"counts_by_year":[{"year":2026,"cited_by_count":5}],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-09-23T00:00:00"}
