{"id":"https://openalex.org/W4206113722","doi":"https://doi.org/10.3390/sym14010080","title":"A Class of Three-Dimensional Subspace Conjugate Gradient Algorithms for Unconstrained Optimization","display_name":"A Class of Three-Dimensional Subspace Conjugate Gradient Algorithms for Unconstrained Optimization","publication_year":2022,"publication_date":"2022-01-05","ids":{"openalex":"https://openalex.org/W4206113722","doi":"https://doi.org/10.3390/sym14010080"},"language":"en","primary_location":{"id":"doi:10.3390/sym14010080","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14010080","pdf_url":"https://www.mdpi.com/2073-8994/14/1/80/pdf?version=1641557609","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/1/80/pdf?version=1641557609","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020438474","display_name":"Jun Huo","orcid":null},"institutions":[{"id":"https://openalex.org/I163732180","display_name":"Guangxi University of Finance and Economics","ror":"https://ror.org/02ayg6516","country_code":"CN","type":"education","lineage":["https://openalex.org/I163732180"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Huo","raw_affiliation_strings":["Guangxi (ASEAN) Financial Research Center, Guangxi University of Finance and Economics, Nanning 530007, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Guangxi (ASEAN) Financial Research Center, Guangxi University of Finance and Economics, Nanning 530007, China","institution_ids":["https://openalex.org/I163732180"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045904477","display_name":"Jielan Yang","orcid":"https://orcid.org/0000-0002-9727-7705"},"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":true,"raw_author_name":"Jielan Yang","raw_affiliation_strings":["School of Mathematics and Information Science, Guangxi University, Nanning 530004, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, Guangxi University, Nanning 530004, China","institution_ids":["https://openalex.org/I150807315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101457292","display_name":"Guoxin Wang","orcid":"https://orcid.org/0000-0003-2363-8595"},"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":"Guoxin Wang","raw_affiliation_strings":["School of Mathematics and Information Science, Guangxi University, Nanning 530004, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, Guangxi University, Nanning 530004, China","institution_ids":["https://openalex.org/I150807315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004738690","display_name":"Shengwei Yao","orcid":"https://orcid.org/0000-0002-0338-4631"},"institutions":[{"id":"https://openalex.org/I163732180","display_name":"Guangxi University of Finance and Economics","ror":"https://ror.org/02ayg6516","country_code":"CN","type":"education","lineage":["https://openalex.org/I163732180"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shengwei Yao","raw_affiliation_strings":["Guangxi (ASEAN) Financial Research Center, Guangxi University of Finance and Economics, Nanning 530007, China","Guangxi Key Laboratory Cultivation Base of Cross-Border E-Commerce Intelligent Information Processing, Guangxi University of Finance and Economics, Nanning 530007, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Guangxi (ASEAN) Financial Research Center, Guangxi University of Finance and Economics, Nanning 530007, China","institution_ids":["https://openalex.org/I163732180"]},{"raw_affiliation_string":"Guangxi Key Laboratory Cultivation Base of Cross-Border E-Commerce Intelligent Information Processing, Guangxi University of Finance and Economics, Nanning 530007, China","institution_ids":["https://openalex.org/I163732180"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5004738690","https://openalex.org/A5045904477"],"corresponding_institution_ids":["https://openalex.org/I150807315","https://openalex.org/I163732180"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.8772,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.64571271,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"14","issue":"1","first_page":"80","last_page":"80"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9957000017166138,"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":0.9891999959945679,"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/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.8166725039482117},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.7609951496124268},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.6685143113136292},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5881699323654175},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5847510695457458},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5655208826065063},{"id":"https://openalex.org/keywords/conjugate-residual-method","display_name":"Conjugate residual method","score":0.537719190120697},{"id":"https://openalex.org/keywords/proximal-gradient-methods","display_name":"Proximal Gradient Methods","score":0.4889041483402252},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.4424605071544647},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.43922674655914307},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4366968870162964},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4194842278957367},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3895944058895111},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.356751024723053},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34482061862945557},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.10727423429489136},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08193004131317139},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07770949602127075}],"concepts":[{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.8166725039482117},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.7609951496124268},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.6685143113136292},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5881699323654175},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5847510695457458},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5655208826065063},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.537719190120697},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.4889041483402252},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.4424605071544647},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.43922674655914307},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4366968870162964},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4194842278957367},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3895944058895111},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.356751024723053},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34482061862945557},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.10727423429489136},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08193004131317139},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07770949602127075},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14010080","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14010080","pdf_url":"https://www.mdpi.com/2073-8994/14/1/80/pdf?version=1641557609","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:79105bc1d3ca433ea1f7b7ad08fdaf2f","is_oa":true,"landing_page_url":"https://doaj.org/article/79105bc1d3ca433ea1f7b7ad08fdaf2f","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 1, p 80 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/1/80/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14010080","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14010080","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14010080","pdf_url":"https://www.mdpi.com/2073-8994/14/1/80/pdf?version=1641557609","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4206113722.pdf"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1497566274","https://openalex.org/W1979539583","https://openalex.org/W2012231377","https://openalex.org/W2014851363","https://openalex.org/W2018215034","https://openalex.org/W2036795720","https://openalex.org/W2051247543","https://openalex.org/W2053799091","https://openalex.org/W2066743741","https://openalex.org/W2075313995","https://openalex.org/W2076605490","https://openalex.org/W2091549324","https://openalex.org/W2149454052","https://openalex.org/W2167137033","https://openalex.org/W2316564661","https://openalex.org/W2340930132","https://openalex.org/W2469503150","https://openalex.org/W2586727428","https://openalex.org/W2767148939","https://openalex.org/W2892724185","https://openalex.org/W2898829052","https://openalex.org/W2921094061","https://openalex.org/W3094968720","https://openalex.org/W3120395271","https://openalex.org/W6663791796","https://openalex.org/W6669248366","https://openalex.org/W6684877539","https://openalex.org/W6703921008"],"related_works":["https://openalex.org/W4319027779","https://openalex.org/W2604655597","https://openalex.org/W2348618647","https://openalex.org/W2390078254","https://openalex.org/W2947596922","https://openalex.org/W1993524345","https://openalex.org/W2364021889","https://openalex.org/W2356365850","https://openalex.org/W2383960336","https://openalex.org/W1999446604"],"abstract_inverted_index":{"In":[0,61],"this":[1],"paper,":[2],"a":[3,28,49],"three-parameter":[4],"subspace":[5],"conjugate":[6],"gradient":[7],"method":[8,51],"is":[9,42,56,67,79],"proposed":[10,65],"for":[11,52],"solving":[12],"large-scale":[13],"unconstrained":[14],"optimization":[15],"problems.":[16],"By":[17],"minimizing":[18],"the":[19,24,33,39,64,76],"quadratic":[20],"approximate":[21],"model":[22],"of":[23,48],"objective":[25],"function":[26],"on":[27],"new":[29],"special":[30],"three-dimensional":[31],"subspace,":[32],"embedded":[34],"parameters":[35],"are":[36],"determined":[37],"and":[38,71,81],"corresponding":[40],"algorithm":[41,66,78],"obtained.":[43],"The":[44],"global":[45],"convergence":[46],"result":[47],"given":[50,77],"general":[53],"nonlinear":[54],"functions":[55],"established":[57],"under":[58],"mild":[59],"assumptions.":[60],"numerical":[62],"experiments,":[63],"compared":[68],"with":[69],"SMCG_NLS":[70],"SMCG_Conic,":[72],"which":[73],"shows":[74],"that":[75],"robust":[80],"efficient.":[82]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
