{"id":"https://openalex.org/W2525623505","doi":"https://doi.org/10.1080/10556788.2016.1225211","title":"Eigenvalues versus singular values study in conjugate gradient algorithms for large-scale unconstrained optimization","display_name":"Eigenvalues versus singular values study in conjugate gradient algorithms for large-scale unconstrained optimization","publication_year":2016,"publication_date":"2016-09-28","ids":{"openalex":"https://openalex.org/W2525623505","doi":"https://doi.org/10.1080/10556788.2016.1225211","mag":"2525623505"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2016.1225211","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2016.1225211","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/A5010606032","display_name":"Neculai Andrei","orcid":null},"institutions":[{"id":"https://openalex.org/I4210114681","display_name":"National Institute for Research & Development in Informatics","ror":"https://ror.org/028rq5v79","country_code":"RO","type":"facility","lineage":["https://openalex.org/I4210114681"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Neculai Andrei","raw_affiliation_strings":["Center for Advanced Modeling and Optimization, Research Institute for Informatics, 8-10 Averescu Avenue, Bucharest 1, Romania"],"affiliations":[{"raw_affiliation_string":"Center for Advanced Modeling and Optimization, Research Institute for Informatics, 8-10 Averescu Avenue, Bucharest 1, Romania","institution_ids":["https://openalex.org/I4210114681"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5010606032"],"corresponding_institution_ids":["https://openalex.org/I4210114681"],"apc_list":null,"apc_paid":null,"fwci":2.7375,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.89504373,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"32","issue":"3","first_page":"534","last_page":"551"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9976000189781189,"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"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9829000234603882,"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":0.8338712453842163},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.8213454484939575},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.6375609636306763},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.6030370593070984},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5986298322677612},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5635241270065308},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5275951027870178},{"id":"https://openalex.org/keywords/descent-direction","display_name":"Descent direction","score":0.44479885697364807},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.43909311294555664},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.4319349229335785},{"id":"https://openalex.org/keywords/derivation-of-the-conjugate-gradient-method","display_name":"Derivation of the conjugate gradient method","score":0.43038231134414673},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.4269677996635437},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.362179696559906},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33319950103759766},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11079826951026917}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8338712453842163},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.8213454484939575},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.6375609636306763},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.6030370593070984},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5986298322677612},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5635241270065308},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5275951027870178},{"id":"https://openalex.org/C116149140","wikidata":"https://www.wikidata.org/wiki/Q2070951","display_name":"Descent direction","level":4,"score":0.44479885697364807},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43909311294555664},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.4319349229335785},{"id":"https://openalex.org/C198562538","wikidata":"https://www.wikidata.org/wiki/Q5262612","display_name":"Derivation of the conjugate gradient method","level":5,"score":0.43038231134414673},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.4269677996635437},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.362179696559906},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33319950103759766},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11079826951026917},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"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/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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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":1,"locations":[{"id":"doi:10.1080/10556788.2016.1225211","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2016.1225211","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W89654658","https://openalex.org/W613054787","https://openalex.org/W640673894","https://openalex.org/W1492771151","https://openalex.org/W1540969907","https://openalex.org/W1555584805","https://openalex.org/W1563835996","https://openalex.org/W1568288633","https://openalex.org/W1967077838","https://openalex.org/W1975024103","https://openalex.org/W1985088446","https://openalex.org/W1987327258","https://openalex.org/W1988849934","https://openalex.org/W2006716496","https://openalex.org/W2009999380","https://openalex.org/W2012231377","https://openalex.org/W2012960907","https://openalex.org/W2014851363","https://openalex.org/W2016518303","https://openalex.org/W2018215034","https://openalex.org/W2035180740","https://openalex.org/W2059327787","https://openalex.org/W2061813658","https://openalex.org/W2064616889","https://openalex.org/W2068484625","https://openalex.org/W2071371660","https://openalex.org/W2072258407","https://openalex.org/W2082479178","https://openalex.org/W2083434008","https://openalex.org/W2084277536","https://openalex.org/W2086108341","https://openalex.org/W2091549324","https://openalex.org/W2091874256","https://openalex.org/W2108560279","https://openalex.org/W2110290705","https://openalex.org/W2116284739","https://openalex.org/W2122565324","https://openalex.org/W2266946488","https://openalex.org/W2316564661","https://openalex.org/W2325195382","https://openalex.org/W2333918876","https://openalex.org/W2471988522","https://openalex.org/W2500965032","https://openalex.org/W2775740332","https://openalex.org/W2979790676","https://openalex.org/W2985272081","https://openalex.org/W4291236916","https://openalex.org/W4300448178"],"related_works":["https://openalex.org/W4319027779","https://openalex.org/W2381924799","https://openalex.org/W2005717169","https://openalex.org/W2384571804","https://openalex.org/W2393037300","https://openalex.org/W2369245602","https://openalex.org/W2060532089","https://openalex.org/W2069731254","https://openalex.org/W256853304","https://openalex.org/W2371658272"],"abstract_inverted_index":{"Two":[0],"different":[1],"approaches":[2,140],"based":[3],"on":[4],"eigenvalues":[5,72],"and":[6,52,113,154,162],"singular":[7],"values":[8],"of":[9,26,30,73,87,118],"the":[10,13,27,31,42,48,53,58,61,64,71,74,82,84,88,91,97,104,119,169,179],"matrix":[11,75,89],"representing":[12,90],"search":[14,43,65,92],"direction":[15,44,66],"in":[16,63],"conjugate":[17,99,106,181],"gradient":[18,100,107,182],"algorithms":[19,120,149,183],"are":[20,150,184],"considered.":[21],"Using":[22],"a":[23,37],"special":[24],"approximation":[25],"inverse":[28],"Hessian":[29],"objective":[32],"function,":[33],"which":[34,45],"depends":[35],"by":[36,69,110,160],"positive":[38],"parameter,":[39],"we":[40,176],"get":[41],"satisfies":[46],"both":[47,138,148],"sufficient":[49],"descent":[50],"condition":[51,85],"Dai\u2013Liao\u2019s":[54],"conjugacy":[55],"condition.":[56],"In":[57,94],"first":[59],"approach":[60,80],"parameter":[62],"is":[67,102,121],"determined":[68],"clustering":[70],"defining":[76],"it.":[77],"The":[78,115],"second":[79],"uses":[81],"minimizing":[83],"number":[86],"direction.":[93],"this":[95],"case":[96],"obtained":[98],"algorithm":[101,108,159],"exactly":[103],"three-term":[105],"proposed":[109],"Zhang,":[111],"Zhou":[112],"Li.":[114],"global":[116],"convergence":[117],"proved":[122],"for":[123],"uniformly":[124],"convex":[125],"functions.":[126],"Intensive":[127],"numerical":[128,143],"experiments,":[129],"using":[130],"800":[131],"unconstrained":[132],"optimization":[133],"test":[134,171],"problems,":[135],"prove":[136,146],"that":[137,147,178],"these":[139],"have":[141],"similar":[142],"performances.":[144],"We":[145],"significantly":[151],"more":[152,155],"efficient":[153],"robust":[156],"than":[157],"CG-DESCENT":[158],"Hager":[161],"Zhang.":[163],"By":[164],"solving":[165],"five":[166],"applications":[167],"from":[168],"MINPACK-2":[170],"problem":[172],"collection,":[173],"with":[174],"variables,":[175],"show":[177],"suggested":[180],"top":[185],"performer":[186],"versus":[187],"CG-DESCENT.":[188]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
