{"id":"https://openalex.org/W4284894138","doi":"https://doi.org/10.3390/sym14071401","title":"A Scaled Dai\u2013Yuan Projection-Based Conjugate Gradient Method for Solving Monotone Equations with Applications","display_name":"A Scaled Dai\u2013Yuan Projection-Based Conjugate Gradient Method for Solving Monotone Equations with Applications","publication_year":2022,"publication_date":"2022-07-07","ids":{"openalex":"https://openalex.org/W4284894138","doi":"https://doi.org/10.3390/sym14071401"},"language":"en","primary_location":{"id":"doi:10.3390/sym14071401","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14071401","pdf_url":"https://www.mdpi.com/2073-8994/14/7/1401/pdf?version=1657197809","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/2073-8994/14/7/1401/pdf?version=1657197809","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011211798","display_name":"Ali Althobaiti","orcid":"https://orcid.org/0000-0001-6076-625X"},"institutions":[{"id":"https://openalex.org/I179331831","display_name":"Taif University","ror":"https://ror.org/014g1a453","country_code":"SA","type":"education","lineage":["https://openalex.org/I179331831"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ali Althobaiti","raw_affiliation_strings":["Mathematics Department, College of Science, Taif University, Taif 21944, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-6076-625X","affiliations":[{"raw_affiliation_string":"Mathematics Department, College of Science, Taif University, Taif 21944, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073495551","display_name":"Jamilu Sabi\u2019u","orcid":"https://orcid.org/0000-0002-7262-490X"},"institutions":[{"id":"https://openalex.org/I4210099431","display_name":"Maitama Sule University Kano","ror":"https://ror.org/011wymc20","country_code":"NG","type":"education","lineage":["https://openalex.org/I4210099431"]}],"countries":["NG"],"is_corresponding":false,"raw_author_name":"Jamilu Sabi\u2019u","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Yusuf Maitama Sule University, Kano P.M.B. 3099, Nigeria"],"raw_orcid":"https://orcid.org/0000-0002-7262-490X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Yusuf Maitama Sule University, Kano P.M.B. 3099, Nigeria","institution_ids":["https://openalex.org/I4210099431"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057055069","display_name":"Homan Emadifar","orcid":"https://orcid.org/0000-0002-8034-1475"},"institutions":[{"id":"https://openalex.org/I4210089026","display_name":"Islamic Azad University of Hamedan","ror":"https://ror.org/007zpd132","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I4210089026"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Homan Emadifar","raw_affiliation_strings":["Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan 1584743311, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan 1584743311, Iran","institution_ids":["https://openalex.org/I4210089026"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084536914","display_name":"Prem Junsawang","orcid":"https://orcid.org/0000-0003-0468-1862"},"institutions":[{"id":"https://openalex.org/I179193067","display_name":"Khon Kaen University","ror":"https://ror.org/03cq4gr50","country_code":"TH","type":"education","lineage":["https://openalex.org/I179193067"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Prem Junsawang","raw_affiliation_strings":["Department of Statistics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand","institution_ids":["https://openalex.org/I179193067"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035042448","display_name":"Soubhagya Kumar Sahoo","orcid":"https://orcid.org/0000-0003-4524-1951"},"institutions":[{"id":"https://openalex.org/I193073490","display_name":"Siksha O Anusandhan University","ror":"https://ror.org/056ep7w45","country_code":"IN","type":"education","lineage":["https://openalex.org/I193073490"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Soubhagya Kumar Sahoo","raw_affiliation_strings":["Department of Mathematics, Institute of Technical Education and Research, Siksha O Anusandhan University, Bhubaneswar 751030, India"],"raw_orcid":"https://orcid.org/0000-0003-4524-1951","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Institute of Technical Education and Research, Siksha O Anusandhan University, Bhubaneswar 751030, India","institution_ids":["https://openalex.org/I193073490"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5084536914"],"corresponding_institution_ids":["https://openalex.org/I179193067"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":1.1217,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.71017805,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"14","issue":"7","first_page":"1401","last_page":"1401"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9997000098228455,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9997000098228455,"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/T11105","display_name":"Advanced Image Processing Techniques","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9919000267982483,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/line-search","display_name":"Line search","score":0.7905756235122681},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.7737834453582764},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.7364807724952698},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6034221053123474},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5980015993118286},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.545940637588501},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.5385230183601379},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.49941182136535645},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.496340811252594},{"id":"https://openalex.org/keywords/projection-method","display_name":"Projection method","score":0.4934064447879791},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.48460444808006287},{"id":"https://openalex.org/keywords/descent-direction","display_name":"Descent direction","score":0.4712153971195221},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.4562477171421051},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42123210430145264},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39262744784355164},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36983057856559753},{"id":"https://openalex.org/keywords/dykstras-projection-algorithm","display_name":"Dykstra's projection algorithm","score":0.24134495854377747},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09464457631111145},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.0680718719959259}],"concepts":[{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.7905756235122681},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.7737834453582764},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.7364807724952698},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6034221053123474},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5980015993118286},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.545940637588501},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.5385230183601379},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49941182136535645},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.496340811252594},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.4934064447879791},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.48460444808006287},{"id":"https://openalex.org/C116149140","wikidata":"https://www.wikidata.org/wiki/Q2070951","display_name":"Descent direction","level":4,"score":0.4712153971195221},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.4562477171421051},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42123210430145264},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39262744784355164},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36983057856559753},{"id":"https://openalex.org/C202426404","wikidata":"https://www.wikidata.org/wiki/Q5318686","display_name":"Dykstra's projection algorithm","level":2,"score":0.24134495854377747},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09464457631111145},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0680718719959259},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14071401","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14071401","pdf_url":"https://www.mdpi.com/2073-8994/14/7/1401/pdf?version=1657197809","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:a7a98cde827f4cacbbbb779dfab25f91","is_oa":true,"landing_page_url":"https://doaj.org/article/a7a98cde827f4cacbbbb779dfab25f91","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 7, p 1401 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/7/1401/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14071401","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/sym14071401","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14071401","pdf_url":"https://www.mdpi.com/2073-8994/14/7/1401/pdf?version=1657197809","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":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4284894138.pdf"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W1852120790","https://openalex.org/W1977194936","https://openalex.org/W1986350092","https://openalex.org/W2000500538","https://openalex.org/W2009702064","https://openalex.org/W2018794399","https://openalex.org/W2019015034","https://openalex.org/W2020659205","https://openalex.org/W2048992473","https://openalex.org/W2076605490","https://openalex.org/W2083042020","https://openalex.org/W2091549324","https://openalex.org/W2100556411","https://openalex.org/W2109449402","https://openalex.org/W2138601654","https://openalex.org/W2149454052","https://openalex.org/W2166308223","https://openalex.org/W2959870036","https://openalex.org/W3007377825","https://openalex.org/W3009353158","https://openalex.org/W3017234272","https://openalex.org/W3018197199","https://openalex.org/W3033341911","https://openalex.org/W3046706351","https://openalex.org/W3046970259","https://openalex.org/W3080976813","https://openalex.org/W3110947471","https://openalex.org/W3119007564","https://openalex.org/W3136164075","https://openalex.org/W3148296099","https://openalex.org/W3169461471","https://openalex.org/W4200482974","https://openalex.org/W4200556553","https://openalex.org/W4214559405","https://openalex.org/W4229010643","https://openalex.org/W6776539895","https://openalex.org/W6799187738"],"related_works":["https://openalex.org/W2349115186","https://openalex.org/W3107945686","https://openalex.org/W2018215034","https://openalex.org/W2381924799","https://openalex.org/W3096592575","https://openalex.org/W2962081168","https://openalex.org/W2384571804","https://openalex.org/W2740794930","https://openalex.org/W2371658272","https://openalex.org/W2760200308"],"abstract_inverted_index":{"In":[0],"this":[1,97],"paper,":[2],"we":[3,70],"propose":[4,71],"two":[5,34],"scaled":[6],"Dai\u2013Yuan":[7],"(DY)":[8],"directions":[9,18],"for":[10,37,76],"solving":[11,77],"constrained":[12,78],"monotone":[13,79],"nonlinear":[14,80],"systems.":[15],"The":[16,45,93],"proposed":[17,33,49,118],"satisfy":[19],"the":[20,26,39,52,56,62,65,90,112,117],"sufficient":[21],"descent":[22],"condition":[23],"independent":[24],"of":[25,64,96],"line":[27],"search":[28],"strategy.":[29,68],"We":[30],"also":[31,100],"reasonably":[32],"different":[35],"relations":[36],"computing":[38],"scaling":[40],"parameter":[41],"at":[42],"every":[43],"iteration.":[44],"first":[46],"relation":[47],"is":[48,59,99,120],"by":[50,60],"approaching":[51],"quasi-Newton":[53],"direction,":[54],"and":[55,88],"second":[57],"one":[58],"taking":[61],"advantage":[63],"popular":[66],"Barzilai\u2013Borwein":[67],"Moreover,":[69],"a":[72,107],"robust":[73],"projection-based":[74],"algorithm":[75,98,119],"equations":[81],"with":[82,111],"applications":[83],"in":[84],"signal":[85],"restoration":[86],"problems":[87],"reconstructing":[89],"blurred":[91],"images.":[92],"global":[94],"convergence":[95],"provided,":[101],"using":[102],"some":[103],"mild":[104],"assumptions.":[105],"Finally,":[106],"comprehensive":[108],"numerical":[109],"comparison":[110],"relevant":[113],"algorithms":[114],"shows":[115],"that":[116],"efficient.":[121]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2025-10-10T00:00:00"}
