{"id":"https://openalex.org/W4416014902","doi":"https://doi.org/10.1016/j.ejco.2026.100128","title":"A fast Newton method under local Lipschitz smoothness","display_name":"A fast Newton method under local Lipschitz smoothness","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W4416014902","doi":"https://doi.org/10.1016/j.ejco.2026.100128"},"language":"en","primary_location":{"id":"doi:10.1016/j.ejco.2026.100128","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.ejco.2026.100128","pdf_url":null,"source":{"id":"https://openalex.org/S4210171502","display_name":"EURO Journal on Computational Optimization","issn_l":"2192-4406","issn":["2192-4406","2192-4414"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EURO Journal on Computational Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1016/j.ejco.2026.100128","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Serge Gratton","orcid":"https://orcid.org/0000-0002-5021-2357"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Serge Gratton","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-5021-2357","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049311255","display_name":"Sadok Jerad","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sadok Jerad","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-4892-0514","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5002913605","display_name":"Philippe L. Toint","orcid":"https://orcid.org/0000-0002-6166-1860"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Philippe Toint","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-6166-1860","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1400,"currency":"USD","value_usd":1400},"apc_paid":{"value":1400,"currency":"USD","value_usd":1400},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07558733,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":null,"first_page":"100128","last_page":"100128"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.46459999680519104,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.46459999680519104,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.3163999915122986,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.09809999912977219,"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/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.8611000180244446},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.8540999889373779},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.7562000155448914},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.6315000057220459},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.6252999901771545},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.5702999830245972},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4925999939441681},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.38179999589920044}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8611000180244446},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.8540999889373779},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.7562000155448914},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7075999975204468},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.6315000057220459},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.6252999901771545},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.5702999830245972},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5274999737739563},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4925999939441681},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4494999945163727},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38760000467300415},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.38179999589920044},{"id":"https://openalex.org/C194777461","wikidata":"https://www.wikidata.org/wiki/Q1085860","display_name":"Root-finding algorithm","level":3,"score":0.3781000077724457},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.33809998631477356},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.31949999928474426},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.3172999918460846},{"id":"https://openalex.org/C179127668","wikidata":"https://www.wikidata.org/wiki/Q17086396","display_name":"Newton's method in optimization","level":4,"score":0.30709999799728394},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3061000108718872},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2946999967098236},{"id":"https://openalex.org/C73729460","wikidata":"https://www.wikidata.org/wiki/Q17023339","display_name":"Hessian equation","level":4,"score":0.2897999882698059},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.28769999742507935},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.2581000030040741}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1016/j.ejco.2026.100128","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.ejco.2026.100128","pdf_url":null,"source":{"id":"https://openalex.org/S4210171502","display_name":"EURO Journal on Computational Optimization","issn_l":"2192-4406","issn":["2192-4406","2192-4414"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EURO Journal on Computational Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2505.04807","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2505.04807","pdf_url":"https://arxiv.org/pdf/2505.04807","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:arXiv.org:2505.04807","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2505.04807","pdf_url":"https://arxiv.org/pdf/2505.04807","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:pure.unamur.be:publications/1cc3919f-14e4-4f85-9d58-968cc63bc083","is_oa":true,"landing_page_url":"https://researchportal.unamur.be/en/publications/1cc3919f-14e4-4f85-9d58-968cc63bc083","pdf_url":"https://pure.unamur.be/ws/files/110965839/gjt8.pdf","source":{"id":"https://openalex.org/S4406922457","display_name":"Repository of the University of Namur","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Gratton, S, Jerad, S & Toint, P 2025 'A Fast Newton Method Under Local Lipschitz Smoothness' Arxiv.","raw_type":"workingPaper"},{"id":"pmh:doi:10.48550/arxiv.2505.04807","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2505.04807","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2505.04807","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:10.1016/j.ejco.2026.100128","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.ejco.2026.100128","pdf_url":null,"source":{"id":"https://openalex.org/S4210171502","display_name":"EURO Journal on Computational Optimization","issn_l":"2192-4406","issn":["2192-4406","2192-4414"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EURO Journal on Computational Optimization","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3778207229","display_name":null,"funder_award_id":"PI3A-0004","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3879958799","display_name":null,"funder_award_id":"19-PI3A-0004","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G602161992","display_name":null,"funder_award_id":"ANR-19-PI3A-0004","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8318455765","display_name":null,"funder_award_id":"ANR-19","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320309893","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321920","display_name":"Innovation and Technology Commission","ror":"https://ror.org/04vf9tr09"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"A":[0],"new,":[1],"fast":[2],"second-order":[3,84,102],"method":[4],"is":[5,20,105,111],"proposed":[6,75,141],"that":[7,61],"achieves":[8],"the":[9,24,63,68,80,121,137,140],"optimal":[10,122],"$\\mathcal{O}\\left(|\\log(\u03b5)|\u03b5^{-3/2}\\right)$":[11],"complexity":[12,110],"to":[13,44,60,78,114],"obtain":[14],"first-order":[15],"$\u03b5$-stationary":[16],"points.":[17],"Crucially,":[18],"this":[19],"deduced":[21],"without":[22],"assuming":[23],"standard":[25],"global":[26],"Lipschitz":[27],"Hessian":[28,42],"continuity":[29],"condition,":[30],"but":[31],"only":[32],"using":[33,94],"an":[34,57,91],"appropriate":[35],"local":[36],"smoothness":[37],"requirement.":[38],"The":[39],"algorithm":[40,99],"exploits":[41],"information":[43],"compute":[45],"a":[46,50,117],"Newton":[47,69],"step":[48,53,70],"and":[49,71,108,132],"negative":[51,72],"curvature":[52,73],"when":[54],"needed,":[55],"in":[56,76],"approach":[58],"similar":[59],"of":[62,67,82,89,120,139],"AN2C":[64],"method.Inexact":[65],"versions":[66],"are":[74,87,127],"order":[77],"reduce":[79],"cost":[81],"evaluating":[83],"information.":[85],"Details":[86],"given":[88],"such":[90],"iterative":[92],"implementation":[93],"Krylov":[95,133],"subspaces.":[96],"An":[97],"extended":[98],"for":[100,129],"finding":[101],"critical":[103],"points":[104],"also":[106],"developed":[107],"its":[109],"again":[112],"shown":[113],"be":[115],"within":[116],"log":[118],"factor":[119],"one.":[123],"Initial":[124],"numerical":[125],"experiments":[126],"discussed":[128],"both":[130],"factorised":[131],"variants,":[134],"which":[135],"demonstrate":[136],"competitiveness":[138],"algorithm.":[142]},"counts_by_year":[],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
