{"id":"https://openalex.org/W3003358926","doi":"https://doi.org/10.1137/20m1320651","title":"Greedy Quasi-Newton Methods with Explicit Superlinear Convergence","display_name":"Greedy Quasi-Newton Methods with Explicit Superlinear Convergence","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3003358926","doi":"https://doi.org/10.1137/20m1320651","mag":"3003358926"},"language":"en","primary_location":{"id":"doi:10.1137/20m1320651","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1320651","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2002.00657","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Anton Rodomanov","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Anton Rodomanov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Yurii Nesterov","orcid":"https://orcid.org/0000-0002-0542-8757"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yurii Nesterov","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-0542-8757","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.6181,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.9642538,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"31","issue":"1","first_page":"785","last_page":"811"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.8583999872207642,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.8583999872207642,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.07429999858140945,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.02459999918937683,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.8489999771118164},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.6787999868392944},{"id":"https://openalex.org/keywords/broyden\u2013fletcher\u2013goldfarb\u2013shanno-algorithm","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","score":0.5993000268936157},{"id":"https://openalex.org/keywords/hessian-equation","display_name":"Hessian equation","score":0.5864999890327454},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5109000205993652},{"id":"https://openalex.org/keywords/greedy-algorithm","display_name":"Greedy algorithm","score":0.48159998655319214},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.47029998898506165},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4537000060081482}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8626999855041504},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.8489999771118164},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.6787999868392944},{"id":"https://openalex.org/C132721684","wikidata":"https://www.wikidata.org/wiki/Q2877013","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","level":3,"score":0.5993000268936157},{"id":"https://openalex.org/C73729460","wikidata":"https://www.wikidata.org/wiki/Q17023339","display_name":"Hessian equation","level":4,"score":0.5864999890327454},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5109000205993652},{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.48159998655319214},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.47029998898506165},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4577000141143799},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4537000060081482},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.4075999855995178},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4009000062942505},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.35740000009536743},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.3395000100135803},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33709999918937683},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.33059999346733093},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3257000148296356},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.2858000099658966},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.27559998631477356},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C126221529","wikidata":"https://www.wikidata.org/wiki/Q3116070","display_name":"Greedy randomized adaptive search procedure","level":3,"score":0.2662999927997589},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.26089999079704285}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/20m1320651","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1320651","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:arXiv.org:2002.00657","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.00657","pdf_url":"https://arxiv.org/pdf/2002.00657","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2002.00657","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.00657","pdf_url":"https://arxiv.org/pdf/2002.00657","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4690472590","display_name":null,"funder_award_id":"788368","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"}],"funders":[{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W233281767","https://openalex.org/W2002199316","https://openalex.org/W2005136695","https://openalex.org/W2016729766","https://openalex.org/W2022772618","https://openalex.org/W2026393324","https://openalex.org/W2030405518","https://openalex.org/W2037114197","https://openalex.org/W2038210983","https://openalex.org/W2045968916","https://openalex.org/W2053964895","https://openalex.org/W2056641273","https://openalex.org/W2059338280","https://openalex.org/W2062294426","https://openalex.org/W2078409719","https://openalex.org/W2084236346","https://openalex.org/W2103111465","https://openalex.org/W2112820497","https://openalex.org/W2120439575","https://openalex.org/W2129616681","https://openalex.org/W2151568819","https://openalex.org/W2153532571","https://openalex.org/W2153635508","https://openalex.org/W2295492468","https://openalex.org/W2563719283","https://openalex.org/W2603538444","https://openalex.org/W2804140211"],"related_works":[],"abstract_inverted_index":{"In":[0,25],"this":[1,27],"paper,":[2],"we":[3,77],"study":[4],"greedy":[5,74],"variants":[6],"of":[7,21,49,71,86,99],"quasi-Newton":[8,43,75],"methods.":[9],"They":[10],"are":[11],"based":[12],"on":[13,83,96],"the":[14,22,30,41,47,54,97,100,115],"updating":[15,53],"formulas":[16],"from":[17,114],"a":[18,68,92],"certain":[19,69],"subclass":[20,28],"Broyden":[23],"family.":[24],"particular,":[26],"includes":[29],"well-known":[31],"DFP,":[32],"BFGS":[33],"and":[34],"SR1":[35],"updates.":[36],"However,":[37],"in":[38],"contrast":[39],"to":[40,66,120],"classical":[42],"methods,":[44,76],"which":[45,90],"use":[46],"difference":[48],"successive":[50],"iterates":[51],"for":[52],"Hessian":[55,110],"approximations,":[56],"our":[57],"methods":[58,108],"apply":[59],"basis":[60],"vectors,":[61],"greedily":[62],"selected":[63],"so":[64],"as":[65],"maximize":[67],"measure":[70],"progress.":[72],"For":[73],"establish":[78],"an":[79],"explicit":[80],"non-asymptotic":[81],"bound":[82],"their":[84],"rate":[85],"local":[87],"superlinear":[88],"convergence,":[89],"contains":[91],"contraction":[93],"factor,":[94],"depending":[95],"square":[98],"iteration":[101],"counter.":[102],"We":[103],"also":[104],"show":[105],"that":[106],"these":[107],"produce":[109],"approximations":[111],"whose":[112],"deviation":[113],"exact":[116],"Hessians":[117],"linearly":[118],"convergences":[119],"zero.":[121]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2020-02-07T00:00:00"}