{"id":"https://openalex.org/W2026245502","doi":"https://doi.org/10.1137/040614700","title":"Statistical Quasi-Newton: A New Look at Least Change","display_name":"Statistical Quasi-Newton: A New Look at Least Change","publication_year":2007,"publication_date":"2007-10-24","ids":{"openalex":"https://openalex.org/W2026245502","doi":"https://doi.org/10.1137/040614700","mag":"2026245502"},"language":"en","primary_location":{"id":"doi:10.1137/040614700","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040614700","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015399833","display_name":"Chuanhai Liu","orcid":"https://orcid.org/0000-0003-1919-7280"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chuanhai Liu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5008973629","display_name":"Scott Vander Wiel","orcid":"https://orcid.org/0000-0002-2647-3549"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Scott A. Vander Wiel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0177,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.76009335,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"18","issue":"4","first_page":"1266","last_page":"1285"},"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9973999857902527,"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/hessian-matrix","display_name":"Hessian matrix","score":0.962882936000824},{"id":"https://openalex.org/keywords/broyden\u2013fletcher\u2013goldfarb\u2013shanno-algorithm","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","score":0.9556394815444946},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.8598586320877075},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6622023582458496},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.6314475536346436},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5891516208648682},{"id":"https://openalex.org/keywords/wishart-distribution","display_name":"Wishart distribution","score":0.5545600056648254},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4888738989830017},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4817081093788147},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4437435567378998},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.39636316895484924},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3257591128349304},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3080838918685913},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1993371844291687},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.16992297768592834},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.07015883922576904}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.962882936000824},{"id":"https://openalex.org/C132721684","wikidata":"https://www.wikidata.org/wiki/Q2877013","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","level":3,"score":0.9556394815444946},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.8598586320877075},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6622023582458496},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.6314475536346436},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5891516208648682},{"id":"https://openalex.org/C33962027","wikidata":"https://www.wikidata.org/wiki/Q1930697","display_name":"Wishart distribution","level":3,"score":0.5545600056648254},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4888738989830017},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4817081093788147},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4437435567378998},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.39636316895484924},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3257591128349304},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3080838918685913},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1993371844291687},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.16992297768592834},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.07015883922576904},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/040614700","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040614700","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:CiteSeerX.psu:10.1.1.110.9557","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.110.9557","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.stat.purdue.edu/~chuanhai/docs/sqn.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W63600712","https://openalex.org/W1968553199","https://openalex.org/W1977822596","https://openalex.org/W1983596562","https://openalex.org/W1999496147","https://openalex.org/W2003809942","https://openalex.org/W2005136695","https://openalex.org/W2018624971","https://openalex.org/W2022772618","https://openalex.org/W2024081693","https://openalex.org/W2026393324","https://openalex.org/W2031888062","https://openalex.org/W2033793366","https://openalex.org/W2038210983","https://openalex.org/W2042803051","https://openalex.org/W2045968916","https://openalex.org/W2050435480","https://openalex.org/W2051579519","https://openalex.org/W2056603712","https://openalex.org/W2056641273","https://openalex.org/W2057544288","https://openalex.org/W2063698478","https://openalex.org/W2069828243","https://openalex.org/W2075194837","https://openalex.org/W2077486649","https://openalex.org/W2077658674","https://openalex.org/W2078409719","https://openalex.org/W2086047174","https://openalex.org/W2091917610","https://openalex.org/W2153532571","https://openalex.org/W2989128237","https://openalex.org/W3029645440"],"related_works":["https://openalex.org/W2026245502","https://openalex.org/W4318192194","https://openalex.org/W2070932288","https://openalex.org/W4221162014","https://openalex.org/W2937637171","https://openalex.org/W1964096161","https://openalex.org/W2572889128","https://openalex.org/W3091576739","https://openalex.org/W2892976100","https://openalex.org/W2958624776"],"abstract_inverted_index":{"A":[0],"new":[1,84,161,207],"method":[2,162],"for":[3,50,184],"quasi-Newton":[4,86],"minimization":[5],"outperforms":[6],"BFGS":[7,82,140],"by":[8],"combining":[9],"least-change":[10],"updates":[11,137,171],"of":[12,23,152],"the":[13,30,39,47,75,83,101,108,114,153,160],"Hessian":[14,26,179],"with":[15,70,91,172],"step":[16],"sizes":[17],"estimated":[18,73],"from":[19,74],"a":[20,35,128,156],"Wishart":[21,76],"model":[22],"uncertainty.":[24],"The":[25,121],"update":[27,60],"is":[28,43,68,118],"in":[29,107,155],"Broyden":[31,51,136,174],"family":[32],"but":[33],"uses":[34],"negative":[36],"parameter,":[37],"outside":[38],"convex":[40],"range,":[41],"that":[42,145,191,199],"usually":[44],"regarded":[45],"as":[46,139],"safe":[48],"zone":[49],"updates.":[52],"Although":[53],"full":[54],"Newton":[55],"steps":[56,72],"based":[57],"on":[58,100,113,205],"this":[59,182],"tend":[61,176],"to":[62,81,124,131,177,188],"be":[63],"too":[64,193,201],"long,":[65],"excellent":[66],"performance":[67],"obtained":[69],"shorter":[71],"model.":[77],"In":[78,164],"numerical":[79],"comparisons":[80],"statistical":[85],"(SQN)":[87],"algorithm":[88],"typically":[89],"converges":[90],"about":[92,119],"25%":[93],"fewer":[94],"iterations,":[95],"functions,":[96],"and":[97,141,143,168,181],"gradient":[98],"evaluations":[99],"top":[102],"1/3":[103,115],"hardest":[104],"unconstrained":[105],"problems":[106,117],"CUTE":[109],"library.":[110],"Typical":[111],"improvement":[112],"easiest":[116],"5%.":[120],"framework":[122],"used":[123],"derive":[125],"SQN":[126],"provides":[127],"simple":[129],"way":[130],"understand":[132],"differences":[133],"among":[134],"various":[135],"such":[138],"DFP":[142],"shows":[144],"these":[146,211],"methods":[147],"do":[148],"not":[149],"preserve":[150],"accuracy":[151],"Hessian,":[154],"certain":[157],"sense,":[158],"while":[159],"does.":[163],"fact,":[165],"BFGS,":[166],"DFP,":[167],"all":[169],"other":[170],"nonnegative":[173],"parameters":[175],"inflate":[178],"estimates,":[180],"accounts":[183],"their":[185],"observed":[186],"propensity":[187],"correct":[189],"eigenvalues":[190,198],"are":[192,200],"small":[194],"more":[195],"readily":[196],"than":[197],"large.":[202],"Numerical":[203],"results":[204],"three":[206],"test":[208],"functions":[209],"validate":[210],"conclusions.":[212]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}