{"id":"https://openalex.org/W3098929144","doi":"https://doi.org/10.1007/s10589-021-00277-4","title":"Exact linesearch limited-memory quasi-Newton methods for minimizing a quadratic function","display_name":"Exact linesearch limited-memory quasi-Newton methods for minimizing a quadratic function","publication_year":2021,"publication_date":"2021-04-28","ids":{"openalex":"https://openalex.org/W3098929144","doi":"https://doi.org/10.1007/s10589-021-00277-4","mag":"3098929144"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-021-00277-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-021-00277-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-021-00277-4.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10589-021-00277-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012748674","display_name":"David Ek","orcid":"https://orcid.org/0000-0003-1764-5449"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"David Ek","raw_affiliation_strings":["Optimization and Systems Theory, Department of Mathematics, KTH Royal Institute of Technology, 100 44, Stockholm, Sweden","Optimization and Systems Theory, Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Optimization and Systems Theory, Department of Mathematics, KTH Royal Institute of Technology, 100 44, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"Optimization and Systems Theory, Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033807851","display_name":"Anders Forsgren","orcid":"https://orcid.org/0000-0002-6252-7815"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Anders Forsgren","raw_affiliation_strings":["Optimization and Systems Theory, Department of Mathematics, KTH Royal Institute of Technology, 100 44, Stockholm, Sweden","Optimization and Systems Theory, Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden"],"raw_orcid":"https://orcid.org/0000-0002-6252-7815","affiliations":[{"raw_affiliation_string":"Optimization and Systems Theory, Department of Mathematics, KTH Royal Institute of Technology, 100 44, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"Optimization and Systems Theory, Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5033807851"],"corresponding_institution_ids":["https://openalex.org/I86987016"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0227158,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"79","issue":"3","first_page":"789","last_page":"816"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991000294685364,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9954000115394592,"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":0.953399658203125},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.7334979176521301},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6985080242156982},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6212256550788879},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5917556881904602},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5785834789276123},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.49566948413848877},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.46497559547424316},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.45094773173332214},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.4302383065223694},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.4265376031398773},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3949468433856964},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23680707812309265},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1548217236995697},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05503508448600769}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.953399658203125},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.7334979176521301},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6985080242156982},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6212256550788879},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5917556881904602},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5785834789276123},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.49566948413848877},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46497559547424316},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.45094773173332214},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.4302383065223694},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.4265376031398773},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3949468433856964},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23680707812309265},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1548217236995697},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05503508448600769},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10589-021-00277-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-021-00277-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-021-00277-4.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1809.10590","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1809.10590","pdf_url":"https://arxiv.org/pdf/1809.10590","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"mag:3098929144","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1809.10590.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"pmh:oai:RePEc:spr:coopap:v:79:y:2021:i:3:d:10.1007_s10589-021-00277-4","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10589-021-00277-4","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"doi:10.48550/arxiv.1809.10590","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1809.10590","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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-journal"}],"best_oa_location":{"id":"doi:10.1007/s10589-021-00277-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-021-00277-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-021-00277-4.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8022664490","display_name":null,"funder_award_id":"621-2014-4772","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"}],"funders":[{"id":"https://openalex.org/F4320322509","display_name":"Kungliga Tekniska H\u00f6gskolan","ror":"https://ror.org/026vcq606"},{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3098929144.pdf","grobid_xml":"https://content.openalex.org/works/W3098929144.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W63600712","https://openalex.org/W644650476","https://openalex.org/W1506342804","https://openalex.org/W1966539012","https://openalex.org/W1978245827","https://openalex.org/W1993671884","https://openalex.org/W2022772618","https://openalex.org/W2042803051","https://openalex.org/W2051669046","https://openalex.org/W2057565823","https://openalex.org/W2058839679","https://openalex.org/W2077658674","https://openalex.org/W2122565324","https://openalex.org/W2149454052","https://openalex.org/W2152009788","https://openalex.org/W2316564661","https://openalex.org/W2619618571","https://openalex.org/W2747640960","https://openalex.org/W2798909945","https://openalex.org/W2962802528","https://openalex.org/W2963013355","https://openalex.org/W2964123951","https://openalex.org/W3012317737","https://openalex.org/W3029645440","https://openalex.org/W3098015857","https://openalex.org/W4236796448","https://openalex.org/W6912393748"],"related_works":["https://openalex.org/W3098015857","https://openalex.org/W2963635052","https://openalex.org/W2463007134","https://openalex.org/W1993154450","https://openalex.org/W2962885385","https://openalex.org/W2059444119","https://openalex.org/W2793277954","https://openalex.org/W2992166204","https://openalex.org/W3100989367","https://openalex.org/W1982944912","https://openalex.org/W1969422756","https://openalex.org/W2963952517","https://openalex.org/W1536339659","https://openalex.org/W3019265297","https://openalex.org/W564737510","https://openalex.org/W1998770342","https://openalex.org/W3110761040","https://openalex.org/W2019071950","https://openalex.org/W2171601402","https://openalex.org/W2068484625"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"main":[2],"focus":[3],"in":[4,80,92,125],"this":[5,90],"paper":[6],"is":[7,18],"exact":[8,81],"linesearch":[9],"methods":[10,72,88],"for":[11,64,130],"minimizing":[12],"a":[13,23,61,118],"quadratic":[14,77],"function":[15],"whose":[16],"Hessian":[17,28,123],"positive":[19],"definite.":[20],"We":[21,83],"give":[22,117],"class":[24,59,129],"of":[25,37,45,48,55,67,86,101,104,121,139],"limited-memory":[26,68],"quasi-Newton":[27,69],"approximations":[29,124],"which":[30,107],"generate":[31],"search":[32],"directions":[33],"parallel":[34],"to":[35,43],"those":[36,44],"the":[38,46,53,58,65,87,110,122,126,131],"BFGS":[39],"method,":[40],"or":[41],"equivalently,":[42],"method":[47],"preconditioned":[49],"conjugate":[50],"gradients.":[51],"In":[52,114],"setting":[54],"reduced":[56],"Hessians,":[57],"provides":[60],"dynamical":[62],"framework":[63,91],"construction":[66],"methods.":[70],"These":[71],"attain":[73],"finite":[74,93],"termination":[75],"on":[76,99],"optimization":[78,134],"problems":[79],"arithmetic.":[82],"show":[84],"performance":[85],"within":[89],"precision":[94],"arithmetic":[95],"by":[96],"numerical":[97],"simulations":[98],"sequences":[100],"related":[102],"systems":[103],"linear":[105],"equations,":[106],"originate":[108],"from":[109],"CUTEst":[111],"test":[112],"collection.":[113],"addition,":[115],"we":[116],"compact":[119],"representation":[120,137],"full":[127],"Broyden":[128],"general":[132],"unconstrained":[133],"problem.":[135],"This":[136],"consists":[138],"explicit":[140],"matrices":[141],"and":[142],"gradients":[143],"only":[144],"as":[145],"vector":[146],"components.":[147]},"counts_by_year":[],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}