{"id":"https://openalex.org/W2005855026","doi":"https://doi.org/10.1155/2012/641276","title":"Global Convergence of a Modified Spectral Conjugate Gradient Method","display_name":"Global Convergence of a Modified Spectral Conjugate Gradient Method","publication_year":2011,"publication_date":"2011-12-12","ids":{"openalex":"https://openalex.org/W2005855026","doi":"https://doi.org/10.1155/2012/641276","mag":"2005855026"},"language":"en","primary_location":{"id":"doi:10.1155/2012/641276","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/641276","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/641276.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2012/641276.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Huabin Jiang","orcid":null},"institutions":[{"id":"https://openalex.org/I77396741","display_name":"Hunan University of Technology and Business","ror":"https://ror.org/057cydn08","country_code":"CN","type":"education","lineage":["https://openalex.org/I77396741"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huabin Jiang","raw_affiliation_strings":["Department of Electronic Information Technology, Hunan Vocational College of Commerce, Hunan, Changsha 410205, China","Department of Electronic Information Technology, Hunan Vocational College of Commerce, Hunan, Changsha 410205"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic Information Technology, Hunan Vocational College of Commerce, Hunan, Changsha 410205, China","institution_ids":["https://openalex.org/I77396741"]},{"raw_affiliation_string":"Department of Electronic Information Technology, Hunan Vocational College of Commerce, Hunan, Changsha 410205","institution_ids":["https://openalex.org/I77396741"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101814932","display_name":"Songhai Deng","orcid":"https://orcid.org/0000-0002-5074-4791"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Songhai Deng","raw_affiliation_strings":["School of Mathematical Sciences and Computing Technology, Central South University, Hunan, Changsha 410083, China","School of Mathematical Sciences and Computing Technology, Central South University, Hunan, Changsha 410083"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and Computing Technology, Central South University, Hunan, Changsha 410083, China","institution_ids":["https://openalex.org/I139660479"]},{"raw_affiliation_string":"School of Mathematical Sciences and Computing Technology, Central South University, Hunan, Changsha 410083","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058855232","display_name":"Xiaodong Zheng","orcid":"https://orcid.org/0000-0001-8387-6064"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaodong Zheng","raw_affiliation_strings":["School of Mathematical Sciences and Computing Technology, Central South University, Hunan, Changsha 410083, China","School of Mathematical Sciences and Computing Technology, Central South University, Hunan, Changsha 410083"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and Computing Technology, Central South University, Hunan, Changsha 410083, China","institution_ids":["https://openalex.org/I139660479"]},{"raw_affiliation_string":"School of Mathematical Sciences and Computing Technology, Central South University, Hunan, Changsha 410083","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027095108","display_name":"Zhong Wan","orcid":"https://orcid.org/0000-0003-3652-2460"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhong Wan","raw_affiliation_strings":["School of Mathematical Sciences and Computing Technology, Central South University, Hunan, Changsha 410083, China","School of Mathematical Sciences and Computing Technology, Central South University, Hunan, Changsha 410083"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and Computing Technology, Central South University, Hunan, Changsha 410083, China","institution_ids":["https://openalex.org/I139660479"]},{"raw_affiliation_string":"School of Mathematical Sciences and Computing Technology, Central South University, Hunan, Changsha 410083","institution_ids":["https://openalex.org/I139660479"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5027095108"],"corresponding_institution_ids":["https://openalex.org/I139660479"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":1.8348,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.82913708,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"2012","issue":"1","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":0.9997000098228455,"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":0.9897000193595886,"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":0.9857000112533569,"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":0.8841662406921387},{"id":"https://openalex.org/keywords/derivation-of-the-conjugate-gradient-method","display_name":"Derivation of the conjugate gradient method","score":0.7416632175445557},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7309507131576538},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.7247477769851685},{"id":"https://openalex.org/keywords/conjugate-residual-method","display_name":"Conjugate residual method","score":0.7103830575942993},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.6626220941543579},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6620510816574097},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6546217799186707},{"id":"https://openalex.org/keywords/conjugate","display_name":"Conjugate","score":0.5942801833152771},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.5447855591773987},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4993600845336914},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.48276272416114807},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44966191053390503},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42079460620880127},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3531638979911804},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25196734070777893},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1441778838634491},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.062377363443374634},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05445846915245056},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.047700464725494385}],"concepts":[{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.8841662406921387},{"id":"https://openalex.org/C198562538","wikidata":"https://www.wikidata.org/wiki/Q5262612","display_name":"Derivation of the conjugate gradient method","level":5,"score":0.7416632175445557},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7309507131576538},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.7247477769851685},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.7103830575942993},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.6626220941543579},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6620510816574097},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6546217799186707},{"id":"https://openalex.org/C197336794","wikidata":"https://www.wikidata.org/wiki/Q5161150","display_name":"Conjugate","level":2,"score":0.5942801833152771},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.5447855591773987},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4993600845336914},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.48276272416114807},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44966191053390503},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42079460620880127},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3531638979911804},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25196734070777893},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1441778838634491},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.062377363443374634},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05445846915245056},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.047700464725494385},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2012/641276","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/641276","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/641276.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1329337713","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1329337713","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:641276","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2012/641276.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:146397b3577c4b2aa3e6238bf14ccf7b","is_oa":true,"landing_page_url":"https://doaj.org/article/146397b3577c4b2aa3e6238bf14ccf7b","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":"Journal of Applied Mathematics, Vol 2012 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2012/641276","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/641276","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/641276.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3995056950","display_name":null,"funder_award_id":"70921001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6153432584","display_name":"\u7ba1\u7406\u79d1\u5b66\u4e2d\u591a\u6001\u4e0d\u786e\u5b9a\u6027\u5747\u8861\u95ee\u9898\u53ca\u67d4\u6027\u4f18\u5316\u65b9\u6cd5\u7814\u7a76","funder_award_id":"71071162","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":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2005855026.pdf","grobid_xml":"https://content.openalex.org/works/W2005855026.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W150175414","https://openalex.org/W1970131234","https://openalex.org/W1978621794","https://openalex.org/W1987327258","https://openalex.org/W1989243384","https://openalex.org/W1998169401","https://openalex.org/W2006048156","https://openalex.org/W2014851363","https://openalex.org/W2015768774","https://openalex.org/W2025438420","https://openalex.org/W2027112342","https://openalex.org/W2056603712","https://openalex.org/W2059012394","https://openalex.org/W2085694061","https://openalex.org/W2108560279","https://openalex.org/W2184260687","https://openalex.org/W2326304272","https://openalex.org/W2494779131","https://openalex.org/W3029645440","https://openalex.org/W4253866604","https://openalex.org/W4293775970"],"related_works":["https://openalex.org/W2183734858","https://openalex.org/W4229957265","https://openalex.org/W2358414513","https://openalex.org/W3107945686","https://openalex.org/W2060532089","https://openalex.org/W2381924799","https://openalex.org/W2355738879","https://openalex.org/W2356977358","https://openalex.org/W2375347328","https://openalex.org/W2349115186"],"abstract_inverted_index":{"A":[0],"modified":[1],"spectral":[2,42],"PRP":[3,43],"conjugate":[4,44],"gradient":[5],"method":[6],"is":[7,18,46,57,65],"presented":[8],"for":[9],"solving":[10],"unconstrained":[11],"optimization":[12],"problems.":[13],"The":[14],"constructed":[15],"search":[16,34],"direction":[17,25],"proved":[19],"to":[20,35],"be":[21],"a":[22,40],"sufficiently":[23],"descent":[24],"of":[26,54],"the":[27,37,52,70],"objective":[28],"function.":[29],"With":[30],"an":[31],"Armijo\u2010type":[32],"line":[33],"determinate":[36],"step":[38],"length,":[39],"new":[41],"algorithm":[45,64],"developed.":[47],"Under":[48],"some":[49],"mild":[50],"conditions,":[51],"theory":[53],"global":[55],"convergence":[56],"established.":[58],"Numerical":[59],"results":[60],"demonstrate":[61],"that":[62],"this":[63],"promising,":[66],"particularly,":[67],"compared":[68],"with":[69],"existing":[71],"similar":[72],"ones.":[73]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2025-10-10T00:00:00"}
