{"id":"https://openalex.org/W2997811160","doi":"https://doi.org/10.1155/2019/6378368","title":"Spectral Three-Term Constrained Conjugate Gradient Algorithm for Function Minimizations","display_name":"Spectral Three-Term Constrained Conjugate Gradient Algorithm for Function Minimizations","publication_year":2019,"publication_date":"2019-12-25","ids":{"openalex":"https://openalex.org/W2997811160","doi":"https://doi.org/10.1155/2019/6378368","mag":"2997811160"},"language":"en","primary_location":{"id":"doi:10.1155/2019/6378368","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2019/6378368","pdf_url":"https://downloads.hindawi.com/journals/jam/2019/6378368.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/2019/6378368.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015233677","display_name":"Huda I. Ahmed","orcid":"https://orcid.org/0000-0003-3712-1079"},"institutions":[{"id":"https://openalex.org/I12150220","display_name":"University of Mosul","ror":"https://ror.org/039cf4q47","country_code":"IQ","type":"education","lineage":["https://openalex.org/I12150220"]}],"countries":["IQ"],"is_corresponding":true,"raw_author_name":"Huda I. Ahmed","raw_affiliation_strings":["Department of Operations Researches and Intelligent Techniques, College of Computer Sciences and Mathematics, University of Mosul, Mosul, Iraq"],"raw_orcid":"https://orcid.org/0000-0003-3712-1079","affiliations":[{"raw_affiliation_string":"Department of Operations Researches and Intelligent Techniques, College of Computer Sciences and Mathematics, University of Mosul, Mosul, Iraq","institution_ids":["https://openalex.org/I12150220"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081433170","display_name":"Rana Z. Al-Kawaz","orcid":"https://orcid.org/0000-0002-3087-4310"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rana Z. Al-Kawaz","raw_affiliation_strings":["Department of Mathematics, College of Basic Education, University of Telafer, Mosul, Iraq"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Basic Education, University of Telafer, Mosul, Iraq","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063014322","display_name":"Abbas Al-Bayati","orcid":"https://orcid.org/0000-0002-2941-6945"},"institutions":[{"id":"https://openalex.org/I12150220","display_name":"University of Mosul","ror":"https://ror.org/039cf4q47","country_code":"IQ","type":"education","lineage":["https://openalex.org/I12150220"]}],"countries":["IQ"],"is_corresponding":false,"raw_author_name":"Abbas Y. Al-Bayati","raw_affiliation_strings":["University of Telafer, Mosul, Iraq"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Telafer, Mosul, Iraq","institution_ids":["https://openalex.org/I12150220"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015233677"],"corresponding_institution_ids":["https://openalex.org/I12150220"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":3.569,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.93445262,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2019","issue":null,"first_page":"1","last_page":"6"},"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":0.9944000244140625,"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":0.991599977016449,"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":0.8739668130874634},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.6902440786361694},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6582006216049194},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6319127082824707},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.6093425750732422},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.5638226866722107},{"id":"https://openalex.org/keywords/conjugacy-class","display_name":"Conjugacy class","score":0.5496927499771118},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5334529876708984},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.5144219994544983},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.5112040042877197},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5102534294128418},{"id":"https://openalex.org/keywords/conjugate-residual-method","display_name":"Conjugate residual method","score":0.4820173978805542},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4808812439441681},{"id":"https://openalex.org/keywords/derivation-of-the-conjugate-gradient-method","display_name":"Derivation of the conjugate gradient method","score":0.46824824810028076},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.42835763096809387},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3739405870437622},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28873810172080994},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1106640100479126},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07117682695388794}],"concepts":[{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.8739668130874634},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.6902440786361694},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6582006216049194},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6319127082824707},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.6093425750732422},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.5638226866722107},{"id":"https://openalex.org/C87945829","wikidata":"https://www.wikidata.org/wiki/Q1353233","display_name":"Conjugacy class","level":2,"score":0.5496927499771118},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5334529876708984},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.5144219994544983},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.5112040042877197},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5102534294128418},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.4820173978805542},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4808812439441681},{"id":"https://openalex.org/C198562538","wikidata":"https://www.wikidata.org/wiki/Q5262612","display_name":"Derivation of the conjugate gradient method","level":5,"score":0.46824824810028076},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42835763096809387},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3739405870437622},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28873810172080994},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1106640100479126},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07117682695388794},{"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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1155/2019/6378368","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2019/6378368","pdf_url":"https://downloads.hindawi.com/journals/jam/2019/6378368.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/1590199223","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1590199223","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:6378368","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2019/6378368.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:5f8c3cf781b9407192d301ef49ed17f9","is_oa":true,"landing_page_url":"https://doaj.org/article/5f8c3cf781b9407192d301ef49ed17f9","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 2019 (2019)","raw_type":"article"},{"id":"pmh:oai:hindawi.com:10.1155/2019/6378368","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/6378368","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"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":"","raw_type":"Research Article"}],"best_oa_location":{"id":"doi:10.1155/2019/6378368","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2019/6378368","pdf_url":"https://downloads.hindawi.com/journals/jam/2019/6378368.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":[{"id":"https://openalex.org/F4320318976","display_name":"University of Mosul","ror":"https://ror.org/039cf4q47"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2997811160.pdf","grobid_xml":"https://content.openalex.org/works/W2997811160.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1975024103","https://openalex.org/W1978386996","https://openalex.org/W2012231377","https://openalex.org/W2012960907","https://openalex.org/W2052113316","https://openalex.org/W2066743741","https://openalex.org/W2076396137","https://openalex.org/W2083770700","https://openalex.org/W2087256975","https://openalex.org/W2091874256","https://openalex.org/W2149454052","https://openalex.org/W2316564661","https://openalex.org/W2770694455","https://openalex.org/W2959870036"],"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":{"In":[0],"this":[1],"work,":[2],"we":[3],"tend":[4,59],"to":[5,60],"deal":[6],"within":[7],"the":[8,11,34,38,49,62,67,80,83],"field":[9],"of":[10,15,41,66,82],"constrained":[12,46,75],"optimization":[13,76],"methods":[14],"three-term":[16],"Conjugate":[17],"Gradient":[18],"(CG)":[19],"technique":[20,32,47],"which":[21],"is":[22],"primarily":[23],"based":[24],"on":[25],"Dai\u2013Liao":[26],"(DL)":[27],"formula.":[28,86],"The":[29],"new":[30,68,84],"proposed":[31],"satisfies":[33],"conjugacy":[35],"property":[36,65],"and":[37],"descent":[39],"conditions":[40],"Karush\u2013Kuhn\u2013Tucker":[42],"(K.K.T.).":[43],"Our":[44],"planned":[45,69,85],"uses":[48],"robust":[50],"Wolfe":[51],"line":[52],"search":[53],"condition":[54],"with":[55],"some":[56],"assumptions.":[57],"We":[58],"prove":[61],"global":[63],"convergence":[64],"technique.":[70],"Numeral":[71],"comparisons":[72],"for":[73],"(30-thirty)":[74],"issues":[77],"make":[78],"sure":[79],"effectiveness":[81]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}