{"id":"https://openalex.org/W7220710849","doi":"https://doi.org/10.48550/arxiv.2610.06557","title":"CaCuTe Meets SESOP: Better Theory and Practice with Lipschitz Hessians","display_name":"CaCuTe Meets SESOP: Better Theory and Practice with Lipschitz Hessians","publication_year":2026,"publication_date":"2026-10-05","ids":{"openalex":"https://openalex.org/W7220710849","doi":"https://doi.org/10.48550/arxiv.2610.06557"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.06557","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06557","pdf_url":"https://arxiv.org/pdf/2610.06557","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/2610.06557","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062705466","display_name":"Nazarii Tupitsa","orcid":"https://orcid.org/0000-0002-9005-0129","observed_orcids":["https://orcid.org/0000-0002-9005-0129"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tupitsa, Nazarii","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5062705466"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.6323000192642212,"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":0.6323000192642212,"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":0.329800009727478,"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":0.02199999988079071,"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/cubic-regularization","display_name":"cubic regularization","score":0.9440000057220459},{"id":"https://openalex.org/keywords/backtracking","display_name":"backtracking","score":0.5339999794960022},{"id":"https://openalex.org/keywords/global-convergence-rate","display_name":"global convergence rate","score":0.5580000281333923},{"id":"https://openalex.org/keywords/hessian-vector-product","display_name":"Hessian-vector product","score":0.7419999837875366},{"id":"https://openalex.org/keywords/momentum-method","display_name":"momentum methods","score":0.5299999713897705}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7817000150680542},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7574999928474426},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.6480000019073486},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.6055999994277954},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5439000129699707},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.48170000314712524},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4194999933242798},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4025000035762787},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3693000078201294},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.3675999939441681},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.35249999165534973},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.32589998841285706},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.32519999146461487},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.313400000333786},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.3089999854564667},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.304500013589859},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.2922999858856201},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.2754000127315521},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C164752517","wikidata":"https://www.wikidata.org/wiki/Q5570875","display_name":"Global optimization","level":2,"score":0.25949999690055847},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2572999894618988},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.25679999589920044},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.2531999945640564}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.06557","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06557","pdf_url":"https://arxiv.org/pdf/2610.06557","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.2610.06557","doi":"https://doi.org/10.48550/arxiv.2610.06557","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.06557","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":"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.06557","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06557","pdf_url":"https://arxiv.org/pdf/2610.06557","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/W7220710849.pdf","grobid_xml":"https://content.openalex.org/works/W7220710849.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1502711715","https://openalex.org/W2006903949","https://openalex.org/W2009941369","https://openalex.org/W2017279613","https://openalex.org/W2047151498","https://openalex.org/W2753277175","https://openalex.org/W2917318609","https://openalex.org/W3007545624","https://openalex.org/W3035435403","https://openalex.org/W4229447738","https://openalex.org/W4399812772","https://openalex.org/W4400341935","https://openalex.org/W4412203422","https://openalex.org/W4416257904"],"related_works":["https://openalex.org/W7159684852","https://openalex.org/W4416257904","https://openalex.org/W4416014902","https://openalex.org/W7214803277","https://openalex.org/W3205980973","https://openalex.org/W2344097254","https://openalex.org/W2546420264","https://openalex.org/W1982898729","https://openalex.org/W4399322119","https://openalex.org/W7204105747"],"abstract_inverted_index":{"We":[0,116],"combine":[1],"CaCuTe":[2],"with":[3,27,95,148],"sequential":[4],"subspace":[5],"optimization":[6],"(SESOP)":[7],"for":[8,120,139],"smooth":[9],"convex":[10],"minimization":[11,46,54],"under":[12],"Lipschitz":[13],"continuity":[14],"of":[15,31,40,47,55],"the":[16,23,48,79,82,99,103,108,114,126,133,140],"Hessian.":[17],"The":[18,70],"resulting":[19],"method,":[20],"CaCuSESOP,":[21],"achieves":[22],"global":[24,134],"rate":[25,94,136],"$O(k^{-2})$":[26,135],"a":[28,56,67],"fixed":[29],"number":[30,105],"Hessian--vector":[32],"products":[33],"per":[34],"iteration,":[35],"while":[36],"removing":[37],"key":[38],"limitations":[39],"classical":[41],"SESOP.":[42],"In":[43],"particular,":[44],"exact":[45],"original":[49],"objective":[50],"is":[51,74,84,111,137],"replaced":[52],"by":[53,76],"low-dimensional":[57],"cubic":[58,71],"upper":[59],"model,":[60],"which":[61],"needs":[62],"only":[63],"be":[64],"solved":[65],"to":[66,113],"computable":[68],"accuracy.":[69],"regularization":[72],"parameter":[73],"selected":[75],"backtracking.":[77],"If":[78],"Hessian":[80],"at":[81],"minimizer":[83],"positive":[85],"definite,":[86],"CaCuSESOP":[87],"automatically":[88],"attains":[89],"an":[90],"accelerated":[91],"local":[92,100],"linear":[93],"complexity":[96],"$O(\\sqrt{\u03ba_\\star}\\log(1/\\varepsilon))$.":[97],"Neither":[98],"strong-convexity":[101],"parameter,":[102],"condition":[104],"$\u03ba_\\star$,":[106],"nor":[107],"optimal":[109,138],"value":[110],"supplied":[112],"algorithm.":[115],"give":[117],"finite":[118],"bounds":[119],"entering":[121],"this":[122],"regime":[123],"and":[124,150],"adapting":[125],"restart":[127],"schedule.":[128],"Finally,":[129],"we":[130],"prove":[131],"that":[132],"considered":[141],"fixed-budget":[142],"gradient/Hessian--vector-product":[143],"linear-span":[144],"oracle":[145],"class,":[146],"even":[147],"momentum":[149],"unrestricted":[151],"memory.":[152]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}