{"id":"https://openalex.org/W4225006974","doi":"https://doi.org/10.1080/10556788.2022.2053970","title":"A symmetric grouped and ordered multi-secant Quasi-Newton update formula","display_name":"A symmetric grouped and ordered multi-secant Quasi-Newton update formula","publication_year":2022,"publication_date":"2022-04-28","ids":{"openalex":"https://openalex.org/W4225006974","doi":"https://doi.org/10.1080/10556788.2022.2053970"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2022.2053970","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2022.2053970","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://biblio.ugent.be/publication/01GPKN6NZ57M4CGK8AZQSE7YBH/file/01GPPHT2686GS229RZ2ZEWCHT7.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030855444","display_name":"Nicolas Boutet","orcid":"https://orcid.org/0000-0003-3459-564X"},"institutions":[{"id":"https://openalex.org/I150517870","display_name":"Royal Military Academy","ror":"https://ror.org/02vmnye06","country_code":"BE","type":"education","lineage":["https://openalex.org/I150517870"]},{"id":"https://openalex.org/I2801227569","display_name":"Ghent University Hospital","ror":"https://ror.org/00xmkp704","country_code":"BE","type":"healthcare","lineage":["https://openalex.org/I2801227569"]},{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Nicolas Boutet","raw_affiliation_strings":["Ghent University","Royal Military Academy","Department of Electromechanical, Systems and Metal Engineering, Ghent University, Ghent, Belgium","Department of Mathematics, Royal Military Academy, Brussels, Belgium"],"raw_orcid":"https://orcid.org/0000-0003-3459-564X","affiliations":[{"raw_affiliation_string":"Ghent University","institution_ids":["https://openalex.org/I2801227569"]},{"raw_affiliation_string":"Royal Military Academy","institution_ids":["https://openalex.org/I150517870"]},{"raw_affiliation_string":"Department of Electromechanical, Systems and Metal Engineering, Ghent University, Ghent, Belgium","institution_ids":["https://openalex.org/I32597200"]},{"raw_affiliation_string":"Department of Mathematics, Royal Military Academy, Brussels, Belgium","institution_ids":["https://openalex.org/I150517870"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086556459","display_name":"Joris Degroote","orcid":"https://orcid.org/0000-0003-4225-1791"},"institutions":[{"id":"https://openalex.org/I2801227569","display_name":"Ghent University Hospital","ror":"https://ror.org/00xmkp704","country_code":"BE","type":"healthcare","lineage":["https://openalex.org/I2801227569"]},{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]},{"id":"https://openalex.org/I4210116480","display_name":"Flanders Make (Belgium)","ror":"https://ror.org/02ndjfz59","country_code":"BE","type":"company","lineage":["https://openalex.org/I4210116480"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Joris Degroote","raw_affiliation_strings":["Flanders Make","Ghent University","Department of Electromechanical, Systems and Metal Engineering, Ghent University, Ghent, Belgium","Flanders Make, Ghent, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Flanders Make","institution_ids":["https://openalex.org/I4210116480"]},{"raw_affiliation_string":"Ghent University","institution_ids":["https://openalex.org/I2801227569"]},{"raw_affiliation_string":"Department of Electromechanical, Systems and Metal Engineering, Ghent University, Ghent, Belgium","institution_ids":["https://openalex.org/I32597200"]},{"raw_affiliation_string":"Flanders Make, Ghent, Belgium","institution_ids":["https://openalex.org/I4210116480"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035555137","display_name":"Rob Haelterman","orcid":"https://orcid.org/0000-0002-1610-2218"},"institutions":[{"id":"https://openalex.org/I150517870","display_name":"Royal Military Academy","ror":"https://ror.org/02vmnye06","country_code":"BE","type":"education","lineage":["https://openalex.org/I150517870"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Rob Haelterman","raw_affiliation_strings":["Royal Military Academy","Department of Mathematics, Royal Military Academy, Brussels, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Royal Military Academy","institution_ids":["https://openalex.org/I150517870"]},{"raw_affiliation_string":"Department of Mathematics, Royal Military Academy, Brussels, Belgium","institution_ids":["https://openalex.org/I150517870"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5030855444"],"corresponding_institution_ids":["https://openalex.org/I150517870","https://openalex.org/I2801227569","https://openalex.org/I32597200"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0538228,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"37","issue":"6","first_page":"1979","last_page":"2000"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9993000030517578,"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":0.9988999962806702,"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/secant-method","display_name":"Secant method","score":0.9254586100578308},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7102182507514954},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.5529334545135498},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5419396758079529},{"id":"https://openalex.org/keywords/newton-fractal","display_name":"Newton fractal","score":0.5057222843170166},{"id":"https://openalex.org/keywords/broyden\u2013fletcher\u2013goldfarb\u2013shanno-algorithm","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","score":0.49826812744140625},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4821626543998718},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4575052261352539},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.44529539346694946},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.4347586929798126},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33083194494247437},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2794256806373596},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22748762369155884},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.08266714215278625}],"concepts":[{"id":"https://openalex.org/C93926214","wikidata":"https://www.wikidata.org/wiki/Q14915286","display_name":"Secant method","level":4,"score":0.9254586100578308},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7102182507514954},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.5529334545135498},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5419396758079529},{"id":"https://openalex.org/C194342247","wikidata":"https://www.wikidata.org/wiki/Q1151001","display_name":"Newton fractal","level":4,"score":0.5057222843170166},{"id":"https://openalex.org/C132721684","wikidata":"https://www.wikidata.org/wiki/Q2877013","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","level":3,"score":0.49826812744140625},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4821626543998718},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4575052261352539},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.44529539346694946},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.4347586929798126},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33083194494247437},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2794256806373596},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22748762369155884},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.08266714215278625},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","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/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","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},{"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/10556788.2022.2053970","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2022.2053970","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},{"id":"pmh:oai:archive.ugent.be:01GPKN6NZ57M4CGK8AZQSE7YBH","is_oa":true,"landing_page_url":"https://biblio.ugent.be/publication/01GPKN6NZ57M4CGK8AZQSE7YBH","pdf_url":"https://biblio.ugent.be/publication/01GPKN6NZ57M4CGK8AZQSE7YBH/file/01GPPHT2686GS229RZ2ZEWCHT7.pdf","source":{"id":"https://openalex.org/S4306400478","display_name":"Ghent University Academic Bibliography (Ghent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I32597200","host_organization_name":"Ghent University","host_organization_lineage":["https://openalex.org/I32597200"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 1029-4937","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:archive.ugent.be:01GPKN6NZ57M4CGK8AZQSE7YBH","is_oa":true,"landing_page_url":"https://biblio.ugent.be/publication/01GPKN6NZ57M4CGK8AZQSE7YBH","pdf_url":"https://biblio.ugent.be/publication/01GPKN6NZ57M4CGK8AZQSE7YBH/file/01GPPHT2686GS229RZ2ZEWCHT7.pdf","source":{"id":"https://openalex.org/S4306400478","display_name":"Ghent University Academic Bibliography (Ghent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I32597200","host_organization_name":"Ghent University","host_organization_lineage":["https://openalex.org/I32597200"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 1029-4937","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4225006974.pdf","grobid_xml":"https://content.openalex.org/works/W4225006974.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W153050556","https://openalex.org/W1520658537","https://openalex.org/W1579664581","https://openalex.org/W1977822596","https://openalex.org/W1985909446","https://openalex.org/W2020588485","https://openalex.org/W2026393324","https://openalex.org/W2050435480","https://openalex.org/W2057565823","https://openalex.org/W2062294426","https://openalex.org/W2075634091","https://openalex.org/W2077541064","https://openalex.org/W2091917610","https://openalex.org/W2095211439","https://openalex.org/W2100514507","https://openalex.org/W2108590855","https://openalex.org/W2118040915","https://openalex.org/W2125916088","https://openalex.org/W2146804885","https://openalex.org/W2149454052","https://openalex.org/W2156466771","https://openalex.org/W2165038258","https://openalex.org/W2173502753","https://openalex.org/W2395188625","https://openalex.org/W2569942938","https://openalex.org/W2754127623","https://openalex.org/W2766870935","https://openalex.org/W2807699648","https://openalex.org/W2963389134","https://openalex.org/W2997476625","https://openalex.org/W3118576835"],"related_works":["https://openalex.org/W4224046108","https://openalex.org/W2105922132","https://openalex.org/W1985487460","https://openalex.org/W2124368230","https://openalex.org/W2986655728","https://openalex.org/W2731844756","https://openalex.org/W2100479853","https://openalex.org/W2097957716","https://openalex.org/W1592546441","https://openalex.org/W2349605439"],"abstract_inverted_index":{"For":[0],"Quasi-Newton":[1,128,170],"methods,":[2],"one":[3,54],"of":[4,14,91,101,125],"the":[5,15,23,39,68,89,178],"most":[6],"important":[7],"challenges":[8],"is":[9,38,104,131,145],"to":[10,22,82,105,115,121,136,176],"find":[11],"an":[12],"estimate":[13],"Jacobian":[16],"matrix":[17],"as":[18,20,132,134],"close":[19,133],"possible":[21,135],"real":[24],"matrix.":[25],"While":[26],"in":[27,35,53,151],"root-finding":[28],"problems":[29],"multi-secant":[30,49,71,179],"methods":[31,41,52],"are":[32,46,73,162],"regularly":[33],"used,":[34],"optimization,":[36],"it":[37,63],"symmetric":[40,51,127,171],"(in":[42],"particular":[43],"BFGS)":[44],"that":[45,67,130,174],"popular.":[47],"Combining":[48],"and":[50,70,87,114,147],"single":[55,96],"update":[56,97,143,172],"formula":[57,144],"would":[58],"combine":[59],"their":[60,111],"benefits.":[61],"However,":[62],"can":[64,148],"be":[65,149],"proved":[66],"symmetry":[69],"property":[72],"generally":[74],"not":[75],"compatible.":[76],"In":[77],"this":[78,85],"paper,":[79],"we":[80],"try":[81,175],"work":[83],"around":[84],"impossibility":[86],"approach":[88,177],"combination":[90],"both":[92],"properties":[93],"into":[94],"a":[95,122,126],"formula.":[98],"The":[99,164],"novelty":[100],"our":[102],"method":[103,129],"group":[106],"secant":[107,139,156],"equations":[108],"based":[109],"on":[110],"relative":[112],"importance":[113],"order":[116],"those":[117],"groups.":[118],"This":[119],"leads":[120],"generic":[123],"formulation":[124,165],"satisfying":[137],"multiple":[138,155],"equations.":[140],"Our":[141],"new":[142],"modular":[146],"used":[150],"different":[152,160,168],"applications":[153],"where":[154],"equations,":[157],"coming":[158],"from":[159],"sources,":[161],"available.":[163],"encompasses":[166],"also":[167],"existing":[169],"formulas":[173],"property.":[180]},"counts_by_year":[],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}