{"id":"https://openalex.org/W2054844981","doi":"https://doi.org/10.1137/s1052623496308801","title":"On Sizing and Shifting the BFGS Update within the Sized-Broyden Family of Secant Updates","display_name":"On Sizing and Shifting the BFGS Update within the Sized-Broyden Family of Secant Updates","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2054844981","doi":"https://doi.org/10.1137/s1052623496308801","mag":"2054844981"},"language":"en","primary_location":{"id":"doi:10.1137/s1052623496308801","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623496308801","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/A5109945612","display_name":"Haruna Yabe","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"H. Yabe","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028438835","display_name":"H\u00e9ctor J. Mart\u00ednez","orcid":"https://orcid.org/0000-0001-9747-0671"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"H. J. Martinez","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108338956","display_name":"R. A. Tapia","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R. A. Tapia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3461,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.63569292,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"15","issue":"1","first_page":"139","last_page":"160"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9991999864578247,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9980999827384949,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/broyden\u2013fletcher\u2013goldfarb\u2013shanno-algorithm","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","score":0.9778280258178711},{"id":"https://openalex.org/keywords/sizing","display_name":"Sizing","score":0.7414210438728333},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6763972043991089},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5750178098678589},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5383310317993164},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.47792869806289673},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.4684600532054901},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4469274878501892},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4319417178630829},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3497021198272705},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3211594820022583},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3183721601963043},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.20523333549499512},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12468695640563965},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11078056693077087},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09292396903038025},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08708131313323975},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.07047995924949646}],"concepts":[{"id":"https://openalex.org/C132721684","wikidata":"https://www.wikidata.org/wiki/Q2877013","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","level":3,"score":0.9778280258178711},{"id":"https://openalex.org/C2777767291","wikidata":"https://www.wikidata.org/wiki/Q1080291","display_name":"Sizing","level":2,"score":0.7414210438728333},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6763972043991089},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5750178098678589},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5383310317993164},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.47792869806289673},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.4684600532054901},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4469274878501892},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4319417178630829},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3497021198272705},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3211594820022583},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3183721601963043},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.20523333549499512},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12468695640563965},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11078056693077087},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09292396903038025},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08708131313323975},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.07047995924949646},{"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/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","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":3,"locations":[{"id":"doi:10.1137/s1052623496308801","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623496308801","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:repository.rice.edu:1911/101824","is_oa":false,"landing_page_url":"https://hdl.handle.net/1911/101824">https://hdl.handle.net/1911/101824</a>.","pdf_url":null,"source":{"id":"https://openalex.org/S4306401268","display_name":"Rice Digital Scholarship Archive (Rice University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74775410","host_organization_name":"Rice University","host_organization_lineage":["https://openalex.org/I74775410"],"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":"Technical report"},{"id":"pmh:oai:scholarship.rice.edu:1911/101824","is_oa":false,"landing_page_url":"http://hdl.handle.net/1911/101824","pdf_url":null,"source":{"id":"https://openalex.org/S4306401268","display_name":"Rice Digital Scholarship Archive (Rice University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74775410","host_organization_name":"Rice University","host_organization_lineage":["https://openalex.org/I74775410"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Technical report"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W105900138","https://openalex.org/W346467014","https://openalex.org/W1892919230","https://openalex.org/W2003046294","https://openalex.org/W2003809942","https://openalex.org/W2010504016","https://openalex.org/W2017014514","https://openalex.org/W2033793366","https://openalex.org/W2035079355","https://openalex.org/W2041285248","https://openalex.org/W2045968916","https://openalex.org/W2046915036","https://openalex.org/W2047425818","https://openalex.org/W2056603712","https://openalex.org/W2061054410","https://openalex.org/W2068484625","https://openalex.org/W2070747239","https://openalex.org/W2077486649","https://openalex.org/W2096304763","https://openalex.org/W2153532571","https://openalex.org/W3175721619"],"related_works":["https://openalex.org/W2013605080","https://openalex.org/W3012383564","https://openalex.org/W2280670759","https://openalex.org/W3210693517","https://openalex.org/W2026245502","https://openalex.org/W2010504016","https://openalex.org/W4318192194","https://openalex.org/W3197176902","https://openalex.org/W4324358988","https://openalex.org/W4293559771"],"abstract_inverted_index":{"In":[0],"a":[1,30,37,47,121,129],"numerical":[2],"study,":[3],"Contreras":[4,83],"and":[5,73,84],"Tapia":[6,85],"demonstrated":[7],"the":[8,13,20,33,40,51,55,102,110,125,142,146,149,158],"value":[9,27],"of":[10,19,32,39,89,94,109,113,124,133,148],"selectively":[11],"sizing":[12,31,67],"BFGS":[14,34,41,56,103],"secant":[15,134],"update.":[16,42],"A":[17],"conclusion":[18],"current":[21],"study":[22],"is":[23,26,58,117,141,152],"that":[24,54,144],"there":[25],"in":[28,86,157],"following":[29],"update":[35,57,104],"with":[36,63],"shifting":[38,74,95],"Our":[43,92,115],"motivation":[44],"for":[45,78],"such":[46],"strategy":[48],"comes":[49],"from":[50,101],"known":[52],"fact":[53],"prone":[59],"to":[60,70,105,154],"producing":[61],"updates":[62],"large":[64],"eigenvalues.":[65],"Hence,":[66],"may":[68],"contribute":[69],"near":[71],"singularity,":[72],"can":[75,96],"help":[76],"compensate":[77],"this":[79],"deficiency.":[80],"We":[81],"follow":[82],"our":[87,137],"form":[88,93,123],"selective":[90],"sizing.":[91],"be":[97],"viewed":[98],"as":[99],"switching":[100],"an":[106],"alternative":[107],"member":[108,147],"Broyden":[111,131],"family":[112,132],"updates.":[114,135],"shift":[116,140],"obtained":[118],"by":[119],"minimizing":[120],"weighted":[122],"Byrd--Nocedal":[126,159],"measure":[127],"over":[128],"sized":[130],"Numerically,":[136],"most":[138],"effective":[139],"one":[143],"gives":[145],"class":[150],"which":[151],"closest":[153],"steepest":[155],"descent":[156],"measure.":[160]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}