{"id":"https://openalex.org/W4400086183","doi":"https://doi.org/10.1080/10556788.2024.2364203","title":"Two efficient spectral hybrid CG methods based on memoryless BFGS direction and Dai\u2013Liao conjugacy condition","display_name":"Two efficient spectral hybrid CG methods based on memoryless BFGS direction and Dai\u2013Liao conjugacy condition","publication_year":2024,"publication_date":"2024-06-27","ids":{"openalex":"https://openalex.org/W4400086183","doi":"https://doi.org/10.1080/10556788.2024.2364203"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2024.2364203","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2024.2364203","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/A5101804509","display_name":"Pengjie Liu","orcid":"https://orcid.org/0000-0002-9176-6321"},"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"]},{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN","HK"],"is_corresponding":false,"raw_author_name":"Pengjie Liu","raw_affiliation_strings":["Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, People's Republic of China","School of Mathematics, Jiangsu Center for Applied Mathematics (CUMT), China University of Mining and Technology, Xuzhou, Jiangsu, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, People's Republic of China","institution_ids":["https://openalex.org/I14243506"]},{"raw_affiliation_string":"School of Mathematics, Jiangsu Center for Applied Mathematics (CUMT), China University of Mining and Technology, Xuzhou, Jiangsu, People's Republic of China","institution_ids":["https://openalex.org/I25757504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112913921","display_name":"Zihang Yuan","orcid":null},"institutions":[{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zihang Yuan","raw_affiliation_strings":["School of Mathematics, Jiangsu Center for Applied Mathematics (CUMT), China University of Mining and Technology, Xuzhou, Jiangsu, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Jiangsu Center for Applied Mathematics (CUMT), China University of Mining and Technology, Xuzhou, Jiangsu, People's Republic of China","institution_ids":["https://openalex.org/I25757504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058079312","display_name":"Yue Zhuo","orcid":"https://orcid.org/0009-0002-6300-8141"},"institutions":[{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yue Zhuo","raw_affiliation_strings":["School of Mathematics, Jiangsu Center for Applied Mathematics (CUMT), China University of Mining and Technology, Xuzhou, Jiangsu, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Jiangsu Center for Applied Mathematics (CUMT), China University of Mining and Technology, Xuzhou, Jiangsu, People's Republic of China","institution_ids":["https://openalex.org/I25757504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108536856","display_name":"Hu Shao","orcid":null},"institutions":[{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hu Shao","raw_affiliation_strings":["School of Mathematics, Jiangsu Center for Applied Mathematics (CUMT), China University of Mining and Technology, Xuzhou, Jiangsu, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Jiangsu Center for Applied Mathematics (CUMT), China University of Mining and Technology, Xuzhou, Jiangsu, People's Republic of China","institution_ids":["https://openalex.org/I25757504"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5108536856"],"corresponding_institution_ids":["https://openalex.org/I25757504"],"apc_list":null,"apc_paid":null,"fwci":7.5038,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.98601363,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"39","issue":"6","first_page":"1445","last_page":"1463"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9970999956130981,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9970999956130981,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9908000230789185,"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/broyden\u2013fletcher\u2013goldfarb\u2013shanno-algorithm","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","score":0.9385058283805847},{"id":"https://openalex.org/keywords/conjugacy-class","display_name":"Conjugacy class","score":0.8433184623718262},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8278156518936157},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3845062851905823},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37696152925491333},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.355207234621048},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3455459475517273},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.120186448097229},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.05738729238510132}],"concepts":[{"id":"https://openalex.org/C132721684","wikidata":"https://www.wikidata.org/wiki/Q2877013","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","level":3,"score":0.9385058283805847},{"id":"https://openalex.org/C87945829","wikidata":"https://www.wikidata.org/wiki/Q1353233","display_name":"Conjugacy class","level":2,"score":0.8433184623718262},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8278156518936157},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3845062851905823},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37696152925491333},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.355207234621048},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3455459475517273},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.120186448097229},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.05738729238510132},{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556788.2024.2364203","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2024.2364203","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":[{"id":"https://openalex.org/G3485335582","display_name":null,"funder_award_id":"72071202","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W89654658","https://openalex.org/W1565013069","https://openalex.org/W1864714722","https://openalex.org/W1968553199","https://openalex.org/W1979347641","https://openalex.org/W1981912021","https://openalex.org/W2012231377","https://openalex.org/W2018215034","https://openalex.org/W2031891766","https://openalex.org/W2032668178","https://openalex.org/W2036795720","https://openalex.org/W2056603712","https://openalex.org/W2061054410","https://openalex.org/W2064851697","https://openalex.org/W2066743741","https://openalex.org/W2075313995","https://openalex.org/W2091549324","https://openalex.org/W2091874256","https://openalex.org/W2108560279","https://openalex.org/W2149454052","https://openalex.org/W2158894942","https://openalex.org/W2316564661","https://openalex.org/W2340930132","https://openalex.org/W2789787065","https://openalex.org/W2790222781","https://openalex.org/W2797084906","https://openalex.org/W2797447965","https://openalex.org/W3015371390","https://openalex.org/W3206483331","https://openalex.org/W4212997115","https://openalex.org/W4220987265","https://openalex.org/W4226304901","https://openalex.org/W4320004460","https://openalex.org/W4383958065","https://openalex.org/W6603640814"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2016852760","https://openalex.org/W1972403393","https://openalex.org/W3078710903","https://openalex.org/W2787890441","https://openalex.org/W2050511877","https://openalex.org/W3114286735","https://openalex.org/W2960088919","https://openalex.org/W3128946703","https://openalex.org/W2375120501"],"abstract_inverted_index":{"The":[0],"spectral":[1,100],"conjugate":[2],"gradient":[3],"(CG)":[4],"method":[5],"is":[6,28,62,81],"one":[7],"of":[8,32,44,115,148],"the":[9,41,45,65,68,73,79,84,91,110,116,120,146],"effective":[10,99],"methods":[11,103,108],"for":[12,124],"solving":[13,141],"unconstrained":[14,142],"optimization":[15,143],"problems.":[16],"In":[17],"this":[18],"work,":[19],"we":[20],"introduce":[21],"a":[22,29],"composite":[23,51],"hybrid":[24,36,69,101],"CG":[25,37,52,70,102],"parameter":[26],"which":[27],"convex":[30],"combination":[31,46],"two":[33,54,98],"new":[34],"adaptive":[35],"parameters.":[38],"To":[39],"derive":[40],"optimal":[42],"choice":[43],"coefficient":[47],"in":[48],"our":[49,149],"proposed":[50,107,150],"parameter,":[53],"approaches":[55],"to":[56,63,82,89],"calculating":[57],"it":[58],"are":[59,104,128],"introduced.":[60],"One":[61],"minimize":[64],"distance":[66],"between":[67],"direction":[71,77,93],"and":[72,78,134],"self-scaling":[74],"memoryless":[75],"BFGS":[76],"other":[80],"apply":[83],"Dai\u2013Liao":[85],"conjugacy":[86],"condition.":[87],"Further,":[88],"make":[90],"search":[92],"have":[94],"better":[95],"theoretical":[96],"performance,":[97],"generated.":[105],"Our":[106],"ensure":[109],"sufficient":[111],"descent":[112],"property":[113],"regardless":[114],"line":[117,136],"search.":[118,137],"And":[119],"global":[121],"convergence":[122],"results":[123],"general":[125],"non-convex":[126],"functions":[127],"established":[129],"under":[130],"some":[131],"fundamental":[132],"assumptions":[133],"Wolfe":[135],"Numerical":[138],"experiments":[139],"on":[140],"problems":[144],"illustrate":[145],"effectiveness":[147],"methods.":[151]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":17},{"year":2024,"cited_by_count":2}],"updated_date":"2026-06-14T06:11:07.267592","created_date":"2025-10-10T00:00:00"}
