{"id":"https://openalex.org/W2086108341","doi":"https://doi.org/10.1137/s1052623494268443","title":"Convergence Properties of Nonlinear Conjugate Gradient Methods","display_name":"Convergence Properties of Nonlinear Conjugate Gradient Methods","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2086108341","doi":"https://doi.org/10.1137/s1052623494268443","mag":"2086108341"},"language":"en","primary_location":{"id":"doi:10.1137/s1052623494268443","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623494268443","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":["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/A5109187979","display_name":"Yu\u2010Hong Dai","orcid":"https://orcid.org/0000-0002-6932-9512"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuhong Dai","raw_affiliation_strings":["Chinese Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chinese Academy of Sciences","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113166766","display_name":"Jiye Han","orcid":null},"institutions":[{"id":"https://openalex.org/I4210093841","display_name":"Institute of Applied Mathematics","ror":"https://ror.org/00h9jx107","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210093841","https://openalex.org/I4210124601","https://openalex.org/I4210148470"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Jiye Han","raw_affiliation_strings":["CAS - Institute of Applied Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CAS - Institute of Applied Mathematics","institution_ids":["https://openalex.org/I4210093841"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100654856","display_name":"Guanghui Liu","orcid":"https://orcid.org/0000-0001-5480-6390"},"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":"Guanghui Liu","raw_affiliation_strings":["Northwestern University****"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Northwestern University****","institution_ids":["https://openalex.org/I111979921"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029911976","display_name":"Defeng Sun","orcid":"https://orcid.org/0000-0003-0481-272X"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Defeng Sun","raw_affiliation_strings":["University Of New south Wales"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University Of New south Wales","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100522606","display_name":"Yin Hongxia","orcid":null},"institutions":[{"id":"https://openalex.org/I4210093841","display_name":"Institute of Applied Mathematics","ror":"https://ror.org/00h9jx107","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210093841","https://openalex.org/I4210124601","https://openalex.org/I4210148470"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Hongxia Yin","raw_affiliation_strings":["CAS - Institute of Applied Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CAS - Institute of Applied Mathematics","institution_ids":["https://openalex.org/I4210093841"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107835542","display_name":"Ya-xiang Yuan","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ya-Xiang Yuan","raw_affiliation_strings":["Chinese Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chinese Academy of Sciences","institution_ids":["https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.7447,"has_fulltext":false,"cited_by_count":245,"citation_normalized_percentile":{"value":0.95587189,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"10","issue":"2","first_page":"345","last_page":"358"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9912999868392944,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9853000044822693,"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":0.805147111415863},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.7482683658599854},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7171432375907898},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.7144473195075989},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6343298554420471},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.4809371829032898},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46984997391700745},{"id":"https://openalex.org/keywords/conjugate-residual-method","display_name":"Conjugate residual method","score":0.42313000559806824},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.41861847043037415},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.30837327241897583},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10067620873451233}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.805147111415863},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.7482683658599854},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7171432375907898},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.7144473195075989},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6343298554420471},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.4809371829032898},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46984997391700745},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.42313000559806824},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.41861847043037415},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30837327241897583},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10067620873451233},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s1052623494268443","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623494268443","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:CiteSeerX.psu:10.1.1.46.3262","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.3262","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://lsec.cc.ac.cn/pub/home/yyx/papers/p984-net.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5600000023841858}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W150175414","https://openalex.org/W1979347641","https://openalex.org/W1988849934","https://openalex.org/W1995409333","https://openalex.org/W2004669532","https://openalex.org/W2012231377","https://openalex.org/W2012960907","https://openalex.org/W2091917610","https://openalex.org/W2108560279","https://openalex.org/W2158894942","https://openalex.org/W2230977749","https://openalex.org/W2316564661","https://openalex.org/W2363674510","https://openalex.org/W2386386841","https://openalex.org/W2798766386","https://openalex.org/W3134771994"],"related_works":["https://openalex.org/W2349115186","https://openalex.org/W2968025875","https://openalex.org/W2378491594","https://openalex.org/W3215155234","https://openalex.org/W2350348863","https://openalex.org/W2350706414","https://openalex.org/W937190428","https://openalex.org/W2959000961","https://openalex.org/W1437871868","https://openalex.org/W2379863355"],"abstract_inverted_index":{"Recently,":[0],"important":[1],"contributions":[2],"on":[3,102],"convergence":[4,32,42,74,93,100,124],"studies":[5],"of":[6,44,75,95,113,126,140],"conjugate":[7,76,96],"gradient":[8,77,97],"methods":[9,107],"were":[10],"made":[11],"by":[12,61],"Gilbert":[13,49],"and":[14,46,50,105,128],"Nocedal":[15,51],"[SIAM":[16],"J.":[17],"Optim.,":[18],"2":[19],"(1992),":[20],"pp.":[21],"21--42].":[22],"They":[23],"introduce":[24],"a":[25],"\"sufficient":[26],"descent":[27,56,85,116],"condition\"":[28],"to":[29],"establish":[30],"global":[31,73],"results.":[33],"Although":[34],"this":[35],"condition":[36,86],"is":[37,87],"not":[38,89],"needed":[39,90],"in":[40,91,110],"the":[41,54,72,83,92,103,111,114,120,123,138,141,145,154],"analyses":[43,94],"Newton":[45],"quasi-Newton":[47],"methods,":[48,130],"hint":[52],"that":[53,82,136],"sufficient":[55,84,115],"condition,":[57],"which":[58],"was":[59],"enforced":[60],"their":[62],"two-stage":[63],"line":[64],"search":[65],"algorithm,":[66],"may":[67],"be":[68,151],"crucial":[69],"for":[70,153],"ensuring":[71],"methods.":[78,98,156],"This":[79],"paper":[80],"shows":[81],"actually":[88],"Consequently,":[99],"results":[101],"Fletcher--Reeves-":[104,127],"Polak--Ribi\u00e8re-type":[106,129,155],"are":[108,133],"established":[109],"absence":[112],"condition.":[117],"To":[118],"show":[119],"differences":[121],"between":[122],"properties":[125],"two":[131],"examples":[132],"constructed,":[134],"showing":[135],"neither":[137],"boundedness":[139],"level":[142],"set":[143],"nor":[144],"restriction":[146],"$\\beta_k":[147],"\\geq":[148],"0$":[149],"can":[150],"relaxed":[152]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":20},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":14},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":14},{"year":2013,"cited_by_count":13},{"year":2012,"cited_by_count":11}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
