{"id":"https://openalex.org/W2018215034","doi":"https://doi.org/10.1137/030601880","title":"A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search","display_name":"A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2018215034","doi":"https://doi.org/10.1137/030601880","mag":"2018215034"},"language":"en","primary_location":{"id":"doi:10.1137/030601880","is_oa":false,"landing_page_url":"https://doi.org/10.1137/030601880","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/A5002362913","display_name":"William W. Hager","orcid":"https://orcid.org/0000-0003-3132-7017"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"William W. Hager","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101893795","display_name":"Hongchao Zhang","orcid":"https://orcid.org/0000-0003-2518-6975"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hongchao Zhang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002362913"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":24.6604,"has_fulltext":false,"cited_by_count":1092,"citation_normalized_percentile":{"value":0.99782372,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"16","issue":"1","first_page":"170","last_page":"192"},"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":0.9952999949455261,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9872000217437744,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.9158917665481567},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.8862224817276001},{"id":"https://openalex.org/keywords/broyden\u2013fletcher\u2013goldfarb\u2013shanno-algorithm","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","score":0.8838453888893127},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.860804557800293},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8163204789161682},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6864784359931946},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5998260378837585},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.5992185473442078},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.5172293782234192},{"id":"https://openalex.org/keywords/descent-direction","display_name":"Descent direction","score":0.5109826326370239},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.5048073530197144},{"id":"https://openalex.org/keywords/conjugate-residual-method","display_name":"Conjugate residual method","score":0.4951609671115875},{"id":"https://openalex.org/keywords/derivation-of-the-conjugate-gradient-method","display_name":"Derivation of the conjugate gradient method","score":0.49256330728530884},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46559083461761475},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.43897542357444763},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42869511246681213},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10827428102493286},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0884278416633606}],"concepts":[{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.9158917665481567},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.8862224817276001},{"id":"https://openalex.org/C132721684","wikidata":"https://www.wikidata.org/wiki/Q2877013","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","level":3,"score":0.8838453888893127},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.860804557800293},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8163204789161682},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6864784359931946},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5998260378837585},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.5992185473442078},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.5172293782234192},{"id":"https://openalex.org/C116149140","wikidata":"https://www.wikidata.org/wiki/Q2070951","display_name":"Descent direction","level":4,"score":0.5109826326370239},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.5048073530197144},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.4951609671115875},{"id":"https://openalex.org/C198562538","wikidata":"https://www.wikidata.org/wiki/Q5262612","display_name":"Derivation of the conjugate gradient method","level":5,"score":0.49256330728530884},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46559083461761475},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.43897542357444763},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42869511246681213},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10827428102493286},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0884278416633606},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"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/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/030601880","is_oa":false,"landing_page_url":"https://doi.org/10.1137/030601880","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W54906651","https://openalex.org/W89654658","https://openalex.org/W1565013069","https://openalex.org/W1592546441","https://openalex.org/W1760551737","https://openalex.org/W1968553199","https://openalex.org/W1981831430","https://openalex.org/W1982462108","https://openalex.org/W1988849934","https://openalex.org/W1996090111","https://openalex.org/W2010069926","https://openalex.org/W2010647796","https://openalex.org/W2012231377","https://openalex.org/W2012960907","https://openalex.org/W2014851363","https://openalex.org/W2016518303","https://openalex.org/W2043382734","https://openalex.org/W2050786966","https://openalex.org/W2051434435","https://openalex.org/W2051669046","https://openalex.org/W2062106836","https://openalex.org/W2086108341","https://openalex.org/W2090963365","https://openalex.org/W2091549324","https://openalex.org/W2091874256","https://openalex.org/W2091917610","https://openalex.org/W2108560279","https://openalex.org/W2149454052","https://openalex.org/W2158894942","https://openalex.org/W2171926168","https://openalex.org/W2230977749","https://openalex.org/W2316564661","https://openalex.org/W2320871099","https://openalex.org/W2505936072"],"related_works":["https://openalex.org/W2008374458","https://openalex.org/W3210179682","https://openalex.org/W2427294063","https://openalex.org/W2272058142","https://openalex.org/W2005717169","https://openalex.org/W1984722404","https://openalex.org/W2051800432","https://openalex.org/W3000416633","https://openalex.org/W4313560949","https://openalex.org/W2615612939"],"abstract_inverted_index":{"A":[0,72],"new":[1,73],"nonlinear":[2,29],"conjugate":[3,34,159],"gradient":[4,35,160],"method":[5,25],"and":[6,18,82,158],"an":[7,12,129],"associated":[8],"implementation,":[9],"based":[10],"on":[11],"inexact":[13],"line":[14,22,40,66,74],"search,":[15,23,41],"are":[16,153],"proposed":[17],"analyzed.":[19],"With":[20],"exact":[21],"our":[24,42],"reduces":[26],"to":[27],"a":[28,58,95,98,107,139,142],"version":[30],"of":[31,91,97,141],"the":[32,45,65,69,113,120,125,146,163,168],"Hestenes--Stiefel":[33],"scheme.":[36],"For":[37],"any":[38],"(inexact)":[39],"scheme":[43,76],"satisfies":[44],"descent":[46],"condition":[47],"${\\bf":[48],"g}_k^{\\sf":[49],"T}":[50],"{\\bf":[51],"d}_k":[52],"\\le":[53],"-\\frac{7}{8}":[54],"\\|{\\bf":[55],"g}_k\\|^2$.":[56],"Moreover,":[57],"global":[59],"convergence":[60,108],"result":[61],"is":[62,77,80,86,103],"established":[63],"when":[64],"search":[67,75],"fulfills":[68],"Wolfe":[70,126],"conditions.":[71],"developed":[78],"that":[79,131],"efficient":[81],"highly":[83],"accurate.":[84],"Efficiency":[85],"achieved":[87,104],"by":[88,105,118],"exploiting":[89],"properties":[90],"linear":[92],"interpolants":[93],"in":[94,124,138,167],"neighborhood":[96,140],"local":[99,143],"minimizer.":[100],"High":[101],"accuracy":[102],"using":[106,162],"criterion,":[109],"which":[110],"we":[111],"call":[112],"``approximate":[114],"Wolfe'":[115],"conditions,":[116],"obtained":[117],"replacing":[119],"sufficient":[121,148],"decrease":[122,149],"criterion":[123],"conditions":[127],"with":[128,135,155],"approximation":[130],"can":[132],"be":[133],"evaluated":[134],"greater":[136],"precision":[137],"minimum":[144],"than":[145],"usual":[147],"criterion.":[150],"Numerical":[151],"comparisons":[152],"given":[154],"both":[156],"L-BFGS":[157],"methods":[161],"unconstrained":[164],"optimization":[165],"problems":[166],"CUTE":[169],"library.":[170]},"counts_by_year":[{"year":2026,"cited_by_count":22},{"year":2025,"cited_by_count":75},{"year":2024,"cited_by_count":68},{"year":2023,"cited_by_count":88},{"year":2022,"cited_by_count":85},{"year":2021,"cited_by_count":84},{"year":2020,"cited_by_count":72},{"year":2019,"cited_by_count":59},{"year":2018,"cited_by_count":50},{"year":2017,"cited_by_count":58},{"year":2016,"cited_by_count":50},{"year":2015,"cited_by_count":62},{"year":2014,"cited_by_count":64},{"year":2013,"cited_by_count":45},{"year":2012,"cited_by_count":47}],"updated_date":"2026-04-01T17:29:45.350535","created_date":"2025-10-10T00:00:00"}
