{"id":"https://openalex.org/W2076248199","doi":"https://doi.org/10.1155/2013/286486","title":"A Scaled Conjugate Gradient Method for Solving Monotone Nonlinear Equations with Convex Constraints","display_name":"A Scaled Conjugate Gradient Method for Solving Monotone Nonlinear Equations with Convex Constraints","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2076248199","doi":"https://doi.org/10.1155/2013/286486","mag":"2076248199"},"language":"en","primary_location":{"id":"doi:10.1155/2013/286486","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/286486","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/286486.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/2013/286486.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100777554","display_name":"Sheng Wang","orcid":"https://orcid.org/0000-0002-6788-3368"},"institutions":[{"id":"https://openalex.org/I96478251","display_name":"Hunan Institute of Technology","ror":"https://ror.org/04n3k2k71","country_code":"CN","type":"education","lineage":["https://openalex.org/I96478251"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Sheng Wang","raw_affiliation_strings":["Hunan Institute of Technology, Hengyang, Hunan 421008, China"],"raw_orcid":"https://orcid.org/0000-0002-6788-3368","affiliations":[{"raw_affiliation_string":"Hunan Institute of Technology, Hengyang, Hunan 421008, China","institution_ids":["https://openalex.org/I96478251"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021075517","display_name":"Hong-Bo Guan","orcid":"https://orcid.org/0000-0001-6506-8645"},"institutions":[{"id":"https://openalex.org/I96478251","display_name":"Hunan Institute of Technology","ror":"https://ror.org/04n3k2k71","country_code":"CN","type":"education","lineage":["https://openalex.org/I96478251"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongbo Guan","raw_affiliation_strings":["Hunan Institute of Technology, Hengyang, Hunan 421008, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hunan Institute of Technology, Hengyang, Hunan 421008, China","institution_ids":["https://openalex.org/I96478251"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100777554"],"corresponding_institution_ids":["https://openalex.org/I96478251"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.14527163,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9979000091552734,"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":0.9936000108718872,"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":0.8159565329551697},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.7366394996643066},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.6596205830574036},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6431014537811279},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6086976528167725},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5800021886825562},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.5493370294570923},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5469210743904114},{"id":"https://openalex.org/keywords/derivation-of-the-conjugate-gradient-method","display_name":"Derivation of the conjugate gradient method","score":0.5221834182739258},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5143028497695923},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5086427927017212},{"id":"https://openalex.org/keywords/conjugate-residual-method","display_name":"Conjugate residual method","score":0.5020432472229004},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.48055747151374817},{"id":"https://openalex.org/keywords/projection-method","display_name":"Projection method","score":0.4751424789428711},{"id":"https://openalex.org/keywords/proximal-gradient-methods","display_name":"Proximal Gradient Methods","score":0.4650175869464874},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4435790181159973},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3159548342227936},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1965334415435791},{"id":"https://openalex.org/keywords/dykstras-projection-algorithm","display_name":"Dykstra's projection algorithm","score":0.146549791097641},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.1441388726234436},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06035307049751282}],"concepts":[{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.8159565329551697},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.7366394996643066},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.6596205830574036},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6431014537811279},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6086976528167725},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5800021886825562},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.5493370294570923},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5469210743904114},{"id":"https://openalex.org/C198562538","wikidata":"https://www.wikidata.org/wiki/Q5262612","display_name":"Derivation of the conjugate gradient method","level":5,"score":0.5221834182739258},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5143028497695923},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5086427927017212},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.5020432472229004},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.48055747151374817},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.4751424789428711},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.4650175869464874},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4435790181159973},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3159548342227936},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1965334415435791},{"id":"https://openalex.org/C202426404","wikidata":"https://www.wikidata.org/wiki/Q5318686","display_name":"Dykstra's projection algorithm","level":2,"score":0.146549791097641},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.1441388726234436},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06035307049751282},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/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/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2013/286486","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/286486","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/286486.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/1394808242","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1394808242","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:286486","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2013/286486.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:e132151be6854140a999d5c4d5495cbd","is_oa":true,"landing_page_url":"https://doaj.org/article/e132151be6854140a999d5c4d5495cbd","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 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/286486","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/286486","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/286486.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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2076248199.pdf","grobid_xml":"https://content.openalex.org/works/W2076248199.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1419332566","https://openalex.org/W1977194936","https://openalex.org/W1999855318","https://openalex.org/W2004777087","https://openalex.org/W2014528048","https://openalex.org/W2018794399","https://openalex.org/W2020659205","https://openalex.org/W2035017667","https://openalex.org/W2048992473"],"related_works":["https://openalex.org/W4319027779","https://openalex.org/W2356365850","https://openalex.org/W2383960336","https://openalex.org/W2947596922","https://openalex.org/W2364021889","https://openalex.org/W2348618647","https://openalex.org/W2390078254","https://openalex.org/W2379322359","https://openalex.org/W1999446604","https://openalex.org/W2998601759"],"abstract_inverted_index":{"Based":[0],"on":[1],"the":[2,13,57,60,100],"Scaled":[3],"conjugate":[4,43],"gradient":[5,44],"(SCALCG)":[6],"method":[7,15,25,35,45,48,102],"presented":[8,16],"by":[9,17],"Andrei":[10],"(2007)":[11],"and":[12,19,46,105],"projection":[14],"Solodov":[18],"Svaiter,":[20],"we":[21,87],"propose":[22],"a":[23,40],"SCALCG":[24,34],"for":[26,49,66],"solving":[27,50,67,76],"monotone":[28,78],"nonlinear":[29,79],"equations":[30,80],"with":[31,81],"convex":[32,82],"constraints.":[33,83],"can":[36,72],"be":[37,73],"regarded":[38],"as":[39],"combination":[41],"of":[42,59],"Newton-type":[47],"unconstrained":[51],"optimization":[52],"problems.":[53,69],"So,":[54,70],"it":[55,71],"has":[56],"advantages":[58],"both":[61],"methods.":[62],"It":[63],"is":[64,103],"suitable":[65],"large-scale":[68,77],"applied":[74],"to":[75],"Under":[84],"reasonable":[85],"conditions,":[86],"prove":[88],"its":[89],"global":[90],"convergence.":[91],"We":[92],"also":[93],"do":[94],"some":[95],"numerical":[96],"experiments":[97],"show":[98],"that":[99],"proposed":[101],"efficient":[104],"promising.":[106]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}