{"id":"https://openalex.org/W3092262150","doi":"https://doi.org/10.1137/20m1373190","title":"A Noise-Tolerant Quasi-Newton Algorithm for Unconstrained Optimization","display_name":"A Noise-Tolerant Quasi-Newton Algorithm for Unconstrained Optimization","publication_year":2022,"publication_date":"2022-01-05","ids":{"openalex":"https://openalex.org/W3092262150","doi":"https://doi.org/10.1137/20m1373190","mag":"3092262150"},"language":"en","primary_location":{"id":"doi:10.1137/20m1373190","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1373190","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2010.04352","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057574221","display_name":"Hao-Jun Michael Shi","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hao-Jun M. Shi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102007385","display_name":"Yuchen Xie","orcid":"https://orcid.org/0000-0003-4672-5616"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuchen Xie","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110729604","display_name":"Richard Byrd","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Richard Byrd","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5081856145","display_name":"Jorge Nocedal","orcid":"https://orcid.org/0000-0002-9662-2730"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jorge Nocedal","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5057574221"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9607,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.67009804,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"32","issue":"1","first_page":"29","last_page":"55"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"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":0.9998000264167786,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9965000152587891,"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/broyden\u2013fletcher\u2013goldfarb\u2013shanno-algorithm","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","score":0.9859300851821899},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.8214511871337891},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.6815628409385681},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6210436820983887},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6091232299804688},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.6064194440841675},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5948611497879028},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5475793480873108},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5296026468276978},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4836231768131256},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4638630747795105},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4137859344482422},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.33903199434280396},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32531851530075073},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.2976541519165039},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12159901857376099}],"concepts":[{"id":"https://openalex.org/C132721684","wikidata":"https://www.wikidata.org/wiki/Q2877013","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","level":3,"score":0.9859300851821899},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.8214511871337891},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.6815628409385681},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6210436820983887},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6091232299804688},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.6064194440841675},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5948611497879028},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5475793480873108},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5296026468276978},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4836231768131256},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4638630747795105},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4137859344482422},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.33903199434280396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32531851530075073},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.2976541519165039},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12159901857376099},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1373190","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1373190","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2010.04352","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2010.04352","pdf_url":"https://arxiv.org/pdf/2010.04352","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":"","raw_type":"text"},{"id":"mag:3092262150","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2010.04352.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2010.04352","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2010.04352","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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2010.04352","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2010.04352","pdf_url":"https://arxiv.org/pdf/2010.04352","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1980957423","display_name":null,"funder_award_id":"N00014-14-1-0313","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G3314459484","display_name":"Collaborative Research:   Algorithms for Large-Scale Stochastic and Nonlinear Optimization","funder_award_id":"1620022","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3746155094","display_name":null,"funder_award_id":"DMS-1620070","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4772581387","display_name":null,"funder_award_id":"DMS-1620022","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5834367162","display_name":null,"funder_award_id":"N00014-14-1-0313 P00003","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8464523087","display_name":"Collaborative Research:  Algorithms for Large-scale Stochastic and Nonlinear Optimization","funder_award_id":"1620070","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320308737","display_name":"Facebook","ror":"https://ror.org/01zbnvs85"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3092262150.pdf"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W82751690","https://openalex.org/W90568776","https://openalex.org/W1409984952","https://openalex.org/W1491622225","https://openalex.org/W1969549583","https://openalex.org/W1977405322","https://openalex.org/W2017711521","https://openalex.org/W2035225104","https://openalex.org/W2035992403","https://openalex.org/W2051434435","https://openalex.org/W2055762706","https://openalex.org/W2056621397","https://openalex.org/W2057565823","https://openalex.org/W2085137170","https://openalex.org/W2149479912","https://openalex.org/W2151084831","https://openalex.org/W2153532571","https://openalex.org/W2404678399","https://openalex.org/W2943305848","https://openalex.org/W2947948834","https://openalex.org/W2963477800","https://openalex.org/W2963807877","https://openalex.org/W2963813563","https://openalex.org/W2963941964","https://openalex.org/W2964058036","https://openalex.org/W2979411530","https://openalex.org/W2999729425","https://openalex.org/W3173138228","https://openalex.org/W3173141421"],"related_works":["https://openalex.org/W3001335587","https://openalex.org/W2910666328","https://openalex.org/W2231127213","https://openalex.org/W2971494186","https://openalex.org/W2883309838","https://openalex.org/W3137574707","https://openalex.org/W33665412","https://openalex.org/W2086047174","https://openalex.org/W2235151328","https://openalex.org/W4246756289","https://openalex.org/W2945238055","https://openalex.org/W3098505774","https://openalex.org/W2914786990","https://openalex.org/W2772987450","https://openalex.org/W2328714481","https://openalex.org/W3193576386","https://openalex.org/W2806440755","https://openalex.org/W2187336810","https://openalex.org/W3199991622","https://openalex.org/W2953115460"],"abstract_inverted_index":{"This":[0,21],"paper":[1],"describes":[2],"an":[3],"extension":[4],"of":[5,14,137],"the":[6,12,52,59,74,87,105,119,138],"BFGS":[7,42,75],"and":[8,43,58,71,114],"L-BFGS":[9,44],"methods":[10,45,124,139],"for":[11,131],"minimization":[13],"a":[15,81],"nonlinear":[16],"function":[17],"subject":[18,36],"to":[19,37,100,127],"errors.":[20],"work":[22],"is":[23,77],"motivated":[24],"by":[25,79],"applications":[26],"that":[27,73,84,104],"contain":[28],"computational":[29],"noise,":[30],"employ":[31],"low-precision":[32],"arithmetic,":[33],"or":[34],"are":[35,93,108,125,140],"statistical":[38],"noise.":[39],"The":[40,65,122],"classical":[41],"can":[46,55,62],"fail":[47],"in":[48,116],"such":[49],"circumstances":[50],"because":[51],"updating":[53],"procedure":[54,83],"be":[56],"corrupted":[57],"line":[60,97],"search":[61],"behave":[63],"erratically.":[64],"proposed":[66,123],"method":[67],"addresses":[68],"these":[69],"difficulties":[70],"ensures":[72],"update":[76],"stable":[78],"employing":[80],"lengthening":[82,120],"spaces":[85],"out":[86],"points":[88],"at":[89],"which":[90],"gradient":[91],"differences":[92],"collected.":[94],"A":[95],"new":[96],"search,":[98],"designed":[99],"tolerate":[101],"errors,":[102],"guarantees":[103,130],"Armijo-Wolfe":[106],"conditions":[107],"satisfied":[109],"under":[110],"most":[111],"reasonable":[112],"conditions,":[113],"works":[115],"conjunction":[117],"with":[118,143],"procedure.":[121],"shown":[126],"enjoy":[128],"convergence":[129],"strongly":[132],"convex":[133],"functions.":[134],"Detailed":[135],"implementations":[136],"presented,":[141],"together":[142],"encouraging":[144],"numerical":[145],"results.":[146]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}