{"id":"https://openalex.org/W3173578264","doi":"https://doi.org/10.1007/s40314-021-01557-9","title":"An improved Polak\u2013Ribi\u00e8re\u2013Polyak conjugate gradient method with an efficient restart direction","display_name":"An improved Polak\u2013Ribi\u00e8re\u2013Polyak conjugate gradient method with an efficient restart direction","publication_year":2021,"publication_date":"2021-06-19","ids":{"openalex":"https://openalex.org/W3173578264","doi":"https://doi.org/10.1007/s40314-021-01557-9","mag":"3173578264"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-021-01557-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-021-01557-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","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/A5032551201","display_name":"Xianzhen Jiang","orcid":"https://orcid.org/0000-0001-7727-7583"},"institutions":[{"id":"https://openalex.org/I167274908","display_name":"Guangxi Minzu University","ror":"https://ror.org/0495efn48","country_code":"CN","type":"education","lineage":["https://openalex.org/I167274908"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xianzhen Jiang","raw_affiliation_strings":["College of Mathematics and Physics, Guangxi University for Nationalities, Nanning, 530006, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Physics, Guangxi University for Nationalities, Nanning, 530006, China","institution_ids":["https://openalex.org/I167274908"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066627199","display_name":"Jinbao Jian","orcid":"https://orcid.org/0000-0001-8048-7397"},"institutions":[{"id":"https://openalex.org/I167274908","display_name":"Guangxi Minzu University","ror":"https://ror.org/0495efn48","country_code":"CN","type":"education","lineage":["https://openalex.org/I167274908"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jinbao Jian","raw_affiliation_strings":["College of Mathematics and Physics, Guangxi University for Nationalities, Nanning, 530006, China"],"raw_orcid":"https://orcid.org/0000-0001-8048-7397","affiliations":[{"raw_affiliation_string":"College of Mathematics and Physics, Guangxi University for Nationalities, Nanning, 530006, China","institution_ids":["https://openalex.org/I167274908"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040637139","display_name":"Dan Song","orcid":"https://orcid.org/0000-0002-4096-3333"},"institutions":[{"id":"https://openalex.org/I167274908","display_name":"Guangxi Minzu University","ror":"https://ror.org/0495efn48","country_code":"CN","type":"education","lineage":["https://openalex.org/I167274908"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dan Song","raw_affiliation_strings":["College of Mathematics and Physics, Guangxi University for Nationalities, Nanning, 530006, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Physics, Guangxi University for Nationalities, Nanning, 530006, China","institution_ids":["https://openalex.org/I167274908"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101804509","display_name":"Pengjie Liu","orcid":"https://orcid.org/0000-0002-9176-6321"},"institutions":[{"id":"https://openalex.org/I150807315","display_name":"Guangxi University","ror":"https://ror.org/02c9qn167","country_code":"CN","type":"education","lineage":["https://openalex.org/I150807315"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Pengjie Liu","raw_affiliation_strings":["College of Mathematics and Information Science, Guangxi University, Nanning, 530004, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Guangxi University, Nanning, 530004, China","institution_ids":["https://openalex.org/I150807315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066627199"],"corresponding_institution_ids":["https://openalex.org/I167274908"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":null,"fwci":5.0042,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.96032348,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"40","issue":"5","first_page":null,"last_page":null},"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/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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.8026081323623657},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7200117707252502},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.7190958857536316},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6141802072525024},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.5942772030830383},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5727106332778931},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5519089102745056},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.5195470452308655},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.49154171347618103},{"id":"https://openalex.org/keywords/conjugate","display_name":"Conjugate","score":0.44787344336509705},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.4432125389575958},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4135148525238037},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3526962995529175},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3238562345504761},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09285438060760498},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.06839698553085327},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.061591506004333496},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.053107500076293945},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05079597234725952}],"concepts":[{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.8026081323623657},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7200117707252502},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.7190958857536316},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6141802072525024},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.5942772030830383},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5727106332778931},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5519089102745056},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.5195470452308655},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.49154171347618103},{"id":"https://openalex.org/C197336794","wikidata":"https://www.wikidata.org/wiki/Q5161150","display_name":"Conjugate","level":2,"score":0.44787344336509705},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.4432125389575958},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4135148525238037},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3526962995529175},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3238562345504761},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09285438060760498},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.06839698553085327},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.061591506004333496},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.053107500076293945},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05079597234725952},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-021-01557-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-021-01557-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2500223858","display_name":null,"funder_award_id":"11771383","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8855177069","display_name":null,"funder_award_id":"2020GXNSFDA238017","funder_id":"https://openalex.org/F4320322768","funder_display_name":"Natural Science Foundation of Guangxi Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322768","display_name":"Natural Science Foundation of Guangxi Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W150175414","https://openalex.org/W998640370","https://openalex.org/W2008374458","https://openalex.org/W2012231377","https://openalex.org/W2018215034","https://openalex.org/W2031891766","https://openalex.org/W2053129565","https://openalex.org/W2056603712","https://openalex.org/W2075313995","https://openalex.org/W2081790497","https://openalex.org/W2085137170","https://openalex.org/W2091549324","https://openalex.org/W2098528027","https://openalex.org/W2108560279","https://openalex.org/W2122859623","https://openalex.org/W2130092997","https://openalex.org/W2149454052","https://openalex.org/W2230977749","https://openalex.org/W2236603166","https://openalex.org/W2241952309","https://openalex.org/W2316564661","https://openalex.org/W2340930132","https://openalex.org/W2523851538","https://openalex.org/W2889379562","https://openalex.org/W2891953303","https://openalex.org/W2898257018","https://openalex.org/W2980067177","https://openalex.org/W2999300733","https://openalex.org/W3134771994","https://openalex.org/W4253922247"],"related_works":["https://openalex.org/W2098528027","https://openalex.org/W3197592642","https://openalex.org/W2349115186","https://openalex.org/W2356977358","https://openalex.org/W2384571804","https://openalex.org/W2369191856","https://openalex.org/W2355738879","https://openalex.org/W2371381925","https://openalex.org/W3152814152","https://openalex.org/W2350706414"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}