{"id":"https://openalex.org/W2127547660","doi":"https://doi.org/10.1080/10556780701646360","title":"A new class of quasi-Newton updating formulas","display_name":"A new class of quasi-Newton updating formulas","publication_year":2008,"publication_date":"2008-03-01","ids":{"openalex":"https://openalex.org/W2127547660","doi":"https://doi.org/10.1080/10556780701646360","mag":"2127547660"},"language":"en","primary_location":{"id":"doi:10.1080/10556780701646360","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780701646360","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100336705","display_name":"Donghui Li","orcid":"https://orcid.org/0000-0003-3335-4537"},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Donghui Li","raw_affiliation_strings":["College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, People's Republic of China","College of Mathematics and Econometrics, Hunan University , Changsha, Hunan, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, People's Republic of China","institution_ids":["https://openalex.org/I16609230"]},{"raw_affiliation_string":"College of Mathematics and Econometrics, Hunan University , Changsha, Hunan, People's Republic of China","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011886900","display_name":"Liqun Qi","orcid":"https://orcid.org/0000-0002-1112-5250"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Liqun Qi","raw_affiliation_strings":["Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, Hong Kong","Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I14243506"]},{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048369644","display_name":"Vera Roshchina","orcid":"https://orcid.org/0000-0002-8361-6876"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Vera Roshchina","raw_affiliation_strings":["Department of Mathematics, City University of Hong Kong, Kowloon Tong, Kowloon, Hong Kong","\u2020Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, City University of Hong Kong, Kowloon Tong, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I168719708"]},{"raw_affiliation_string":"\u2020Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100336705"],"corresponding_institution_ids":["https://openalex.org/I16609230"],"apc_list":null,"apc_paid":null,"fwci":0.9847,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.77165951,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"23","issue":"2","first_page":"237","last_page":"249"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9970999956130981,"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":0.9926000237464905,"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/mathematics","display_name":"Mathematics","score":0.7039850950241089},{"id":"https://openalex.org/keywords/broyden\u2013fletcher\u2013goldfarb\u2013shanno-algorithm","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","score":0.6625540256500244},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.6402954459190369},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6205544471740723},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6025257706642151},{"id":"https://openalex.org/keywords/positive-definiteness","display_name":"Positive definiteness","score":0.5875511765480042},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.58099365234375},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5647200345993042},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5447351932525635},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.49565064907073975},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.48357290029525757},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.44389256834983826},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.41969555616378784},{"id":"https://openalex.org/keywords/definiteness","display_name":"Definiteness","score":0.4112923741340637},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.330163836479187},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.23829063773155212},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22493577003479004},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.19456887245178223},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.18894603848457336},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11704564094543457},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06535419821739197}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7039850950241089},{"id":"https://openalex.org/C132721684","wikidata":"https://www.wikidata.org/wiki/Q2877013","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","level":3,"score":0.6625540256500244},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.6402954459190369},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6205544471740723},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6025257706642151},{"id":"https://openalex.org/C2778265155","wikidata":"https://www.wikidata.org/wiki/Q7233276","display_name":"Positive definiteness","level":4,"score":0.5875511765480042},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.58099365234375},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5647200345993042},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5447351932525635},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.49565064907073975},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.48357290029525757},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.44389256834983826},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.41969555616378784},{"id":"https://openalex.org/C2779056149","wikidata":"https://www.wikidata.org/wiki/Q1182686","display_name":"Definiteness","level":2,"score":0.4112923741340637},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.330163836479187},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.23829063773155212},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22493577003479004},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.19456887245178223},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.18894603848457336},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11704564094543457},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06535419821739197},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/10556780701646360","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780701646360","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:ira.lib.polyu.edu.hk:10397/8114","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/8114","pdf_url":null,"source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal/Magazine Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W2045968916","https://openalex.org/W2047307302","https://openalex.org/W2051247543","https://openalex.org/W2056603712","https://openalex.org/W2062294426","https://openalex.org/W2064217481","https://openalex.org/W2095133175","https://openalex.org/W2153532571","https://openalex.org/W2378023240","https://openalex.org/W3141890267","https://openalex.org/W4205795514"],"related_works":["https://openalex.org/W4210436583","https://openalex.org/W2774735586","https://openalex.org/W2383147277","https://openalex.org/W2380066421","https://openalex.org/W1595588025","https://openalex.org/W2380095870","https://openalex.org/W3181246138","https://openalex.org/W2013605080","https://openalex.org/W2377470197","https://openalex.org/W2050642443"],"abstract_inverted_index":{"In":[0],"this":[1,26,77],"paper,":[2],"we":[3,90],"propose":[4,91],"a":[5,12,29,83,92],"derivative-free":[6],"quasi-Newton":[7,16,69,85,94,102],"condition,":[8],"which":[9,97],"results":[10,110],"in":[11,25,76],"new":[13,101],"class":[14,27],"of":[15,38,43,59,68,82],"updating":[17,23,31,62,74,95,105],"formulas":[18,75],"for":[19],"unconstrained":[20],"optimization.":[21],"Each":[22],"formula":[24,32,106],"is":[28,107],"rank-two":[30],"and":[33,79],"preserves":[34],"the":[35,39,44,52,55,60,73,100],"positive":[36],"definiteness":[37],"second":[40],"derivative":[41],"matrix":[42],"quadratic":[45],"model.":[46],"Its":[47],"first":[48,56],"two":[49,57],"terms":[50,58],"are":[51,111],"same":[53],"as":[54],"BFGS":[61],"formula.":[63],"We":[64],"establish":[65],"global":[66],"convergence":[67,81],"methods":[70],"based":[71],"upon":[72],"class,":[78],"superlinear":[80],"special":[84,93],"method":[86],"among":[87],"them.":[88],"Then":[89],"formula,":[96],"repetitively":[98],"uses":[99],"condition.":[103],"This":[104],"derivative-free.":[108],"Numerical":[109],"reported.":[112]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}