{"id":"https://openalex.org/W2058839679","doi":"https://doi.org/10.1007/bf01582063","title":"Representations of quasi-Newton matrices and their use in limited memory methods","display_name":"Representations of quasi-Newton matrices and their use in limited memory methods","publication_year":1994,"publication_date":"1994-01-01","ids":{"openalex":"https://openalex.org/W2058839679","doi":"https://doi.org/10.1007/bf01582063","mag":"2058839679"},"language":"en","primary_location":{"id":"doi:10.1007/bf01582063","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01582063","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","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/A5110661221","display_name":"Richard H. Byrd","orcid":null},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Richard H. Byrd","raw_affiliation_strings":["Computer Science Department, University of Colorado, Boulder, CO, USA","Computer Science Department, University of Colorado Boulder, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Department, University of Colorado, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]},{"raw_affiliation_string":"Computer Science Department, University of Colorado Boulder, USA","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081856145","display_name":"Jorge Nocedal","orcid":"https://orcid.org/0000-0002-9662-2730"},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jorge Nocedal","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, Northwestern University, 60208-3118, Evanston, IL, USA","[Department of Electrical Engineering and Computer Science Northwestern University, Evanston, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, Northwestern University, 60208-3118, Evanston, IL, USA","institution_ids":["https://openalex.org/I111979921"]},{"raw_affiliation_string":"[Department of Electrical Engineering and Computer Science Northwestern University, Evanston, USA]","institution_ids":["https://openalex.org/I111979921"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002119487","display_name":"Robert B. Schnabel","orcid":"https://orcid.org/0000-0003-1707-0294"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert B. Schnabel","raw_affiliation_strings":["Computer Science Department, University of Colorado, Boulder, CO, USA","Computer Science Department, University of Colorado Boulder, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Department, University of Colorado, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]},{"raw_affiliation_string":"Computer Science Department, University of Colorado Boulder, USA","institution_ids":["https://openalex.org/I188538660"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5110661221"],"corresponding_institution_ids":["https://openalex.org/I188538660"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":7.6637,"has_fulltext":false,"cited_by_count":742,"citation_normalized_percentile":{"value":0.97869318,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"63","issue":"1-3","first_page":"129","last_page":"156"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9959999918937683,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9959999918937683,"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":0.7211005687713623},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.669740617275238},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6355423331260681},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6176822185516357},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5887614488601685},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.5403900146484375},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.489926278591156},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4624488651752472},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4357631802558899},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4257437288761139},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4207448661327362},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4085705578327179},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37449419498443604},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.3682060241699219},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3235725462436676},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2662205100059509},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2062494456768036},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13347113132476807},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11846062541007996}],"concepts":[{"id":"https://openalex.org/C132721684","wikidata":"https://www.wikidata.org/wiki/Q2877013","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","level":3,"score":0.7211005687713623},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.669740617275238},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6355423331260681},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6176822185516357},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5887614488601685},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.5403900146484375},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.489926278591156},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4624488651752472},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4357631802558899},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4257437288761139},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4207448661327362},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4085705578327179},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37449419498443604},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.3682060241699219},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3235725462436676},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2662205100059509},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2062494456768036},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13347113132476807},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11846062541007996},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/bf01582063","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01582063","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:ADA454688","is_oa":false,"landing_page_url":"http://oai.dtic.mil/oai/oai?&amp;verb=getRecord&amp;metadataPrefix=html&amp;identifier=ADA454688","pdf_url":null,"source":{"id":"https://openalex.org/S4406923043","display_name":"Defense Technical Information Center (DTIC)","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":"DTIC","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.8.3625","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.8.3625","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ece.northwestern.edu/~nocedal/PSfiles/representations.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.91.1028","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.91.1028","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ece.northwestern.edu/~nocedal/PDFfiles/representations.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":27,"referenced_works":["https://openalex.org/W153050556","https://openalex.org/W1571507592","https://openalex.org/W1586015540","https://openalex.org/W1977822596","https://openalex.org/W1998444222","https://openalex.org/W2000359198","https://openalex.org/W2035002995","https://openalex.org/W2041519450","https://openalex.org/W2048221927","https://openalex.org/W2051434435","https://openalex.org/W2051669046","https://openalex.org/W2068484625","https://openalex.org/W2077658674","https://openalex.org/W2081927732","https://openalex.org/W2090963365","https://openalex.org/W2095211439","https://openalex.org/W2130844535","https://openalex.org/W2145126461","https://openalex.org/W2160332416","https://openalex.org/W2165622925","https://openalex.org/W2478091498","https://openalex.org/W2608505863","https://openalex.org/W3012317737","https://openalex.org/W3124974783","https://openalex.org/W4212997115","https://openalex.org/W4231087723","https://openalex.org/W4299512035"],"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/W4318192194","https://openalex.org/W3197176902","https://openalex.org/W2964248513","https://openalex.org/W4285316332","https://openalex.org/W3159926911"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":14},{"year":2025,"cited_by_count":47},{"year":2024,"cited_by_count":47},{"year":2023,"cited_by_count":33},{"year":2022,"cited_by_count":32},{"year":2021,"cited_by_count":33},{"year":2020,"cited_by_count":32},{"year":2019,"cited_by_count":42},{"year":2018,"cited_by_count":32},{"year":2017,"cited_by_count":34},{"year":2016,"cited_by_count":44},{"year":2015,"cited_by_count":46},{"year":2014,"cited_by_count":34},{"year":2013,"cited_by_count":31},{"year":2012,"cited_by_count":31}],"updated_date":"2026-05-11T08:15:01.531666","created_date":"2025-10-10T00:00:00"}
