{"id":"https://openalex.org/W4224245397","doi":"https://doi.org/10.1155/2022/3527623","title":"A Method of Two New Augmented Lagrange Multiplier Versions for Solving Constrained Problems","display_name":"A Method of Two New Augmented Lagrange Multiplier Versions for Solving Constrained Problems","publication_year":2022,"publication_date":"2022-04-23","ids":{"openalex":"https://openalex.org/W4224245397","doi":"https://doi.org/10.1155/2022/3527623"},"language":"en","primary_location":{"id":"doi:10.1155/2022/3527623","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/3527623","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2022/3527623.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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":"International Journal of Mathematics and Mathematical Sciences","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/ijmms/2022/3527623.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077224048","display_name":"Hamsa Th. Saeed Chilmeran","orcid":"https://orcid.org/0000-0002-2041-5815"},"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":"Hamsa Th. Saeed Chilmeran","raw_affiliation_strings":["Department of Mathematics, College of Computer Sciences and Mathematics, University of Mosul, Mosul, Iraq"],"raw_orcid":"https://orcid.org/0000-0002-2041-5815","affiliations":[{"raw_affiliation_string":"Department of Mathematics, 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/A5081212783","display_name":"Eman T. Hamed","orcid":"https://orcid.org/0000-0002-3487-4297"},"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":"Eman T. Hamed","raw_affiliation_strings":["Department of Operation Researches and Intelligent Techniques, College of Computer Sciences and Mathematics, University of Mosul, Mosul, Iraq"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Operation 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/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":false,"raw_author_name":"Huda I. Ahmed","raw_affiliation_strings":["Department of Operation Researches and Intelligent Techniques, College of Computer Sciences and Mathematics, University of Mosul, Mosul, Iraq"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Operation Researches and Intelligent Techniques, College of Computer Sciences and Mathematics, University of Mosul, Mosul, Iraq","institution_ids":["https://openalex.org/I12150220"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063014322","display_name":"Abbas Al-Bayati","orcid":"https://orcid.org/0000-0002-2941-6945"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Abbas Y. Al-Bayati","raw_affiliation_strings":["University of Telafer, Tall\u2019Afar, Iraq"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Telafer, Tall\u2019Afar, Iraq","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5077224048"],"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":1.9214,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.82655561,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"2022","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":0.9998000264167786,"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":0.9998000264167786,"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":0.9977999925613403,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.8560444712638855},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7921569347381592},{"id":"https://openalex.org/keywords/constraint-algorithm","display_name":"Constraint algorithm","score":0.7021743655204773},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.6342827677726746},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.6316229104995728},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.565010666847229},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.54387366771698},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4903709888458252},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4534466862678528},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.4405522346496582},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17298293113708496}],"concepts":[{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.8560444712638855},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7921569347381592},{"id":"https://openalex.org/C15980293","wikidata":"https://www.wikidata.org/wiki/Q5164368","display_name":"Constraint algorithm","level":3,"score":0.7021743655204773},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.6342827677726746},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.6316229104995728},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.565010666847229},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.54387366771698},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4903709888458252},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4534466862678528},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.4405522346496582},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17298293113708496},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2022/3527623","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/3527623","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2022/3527623.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:3527623","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/ijmms/2022/3527623.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:606f146f358d41748183bfeeedb2accf","is_oa":true,"landing_page_url":"https://doaj.org/article/606f146f358d41748183bfeeedb2accf","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":"International Journal of Mathematics and Mathematical Sciences, Vol 2022 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2022/3527623","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/3527623","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2022/3527623.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.6100000143051147}],"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/W4224245397.pdf","grobid_xml":"https://content.openalex.org/works/W4224245397.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W150175414","https://openalex.org/W1022154690","https://openalex.org/W2012231377","https://openalex.org/W2045319544","https://openalex.org/W2149454052","https://openalex.org/W2487707123","https://openalex.org/W2893506353","https://openalex.org/W2932368967","https://openalex.org/W2933380457","https://openalex.org/W2985471695","https://openalex.org/W2994956981","https://openalex.org/W2997811160","https://openalex.org/W3001353868","https://openalex.org/W3006548334","https://openalex.org/W3027835588","https://openalex.org/W3027988457","https://openalex.org/W3028951152","https://openalex.org/W3034017116","https://openalex.org/W3090682531","https://openalex.org/W3118542069","https://openalex.org/W3127365274","https://openalex.org/W3159557833","https://openalex.org/W7118185362"],"related_works":["https://openalex.org/W2915353907","https://openalex.org/W3017943474","https://openalex.org/W3105202832","https://openalex.org/W2594910400","https://openalex.org/W2964273022","https://openalex.org/W2519328684","https://openalex.org/W4292352742","https://openalex.org/W2058578573","https://openalex.org/W4317581747","https://openalex.org/W2140995069"],"abstract_inverted_index":{"One":[0],"of":[1,6,25,33,41,85,91],"the":[2,9,18,22,26,34,49,53,58,63,77,86,92],"more":[3],"restrictive":[4],"methods":[5],"improvement":[7],"is":[8,52],"augmented":[10],"Lagrange":[11,42],"method.":[12,28],"Two":[13],"versions":[14],"are":[15,83],"built":[16],"in":[17,56,76],"external":[19],"framework":[20,24,55],"and":[21,44,48,89,102],"internal":[23,54],"proposed":[27,35,93],"The":[29,80],"first":[30],"basic":[31],"version":[32,51],"algorithm":[36,60],"includes":[37],"a":[38,71],"new":[39,72],"derivation":[40],"multiples":[43],"different":[45],"penalty":[46],"criteria,":[47],"second":[50],"which":[57],"unconstrained":[59],"known":[61],"as":[62],"conjugate":[64],"gradient":[65],"(CG)":[66],"method":[67],"was":[68,74],"incorporated;":[69],"also,":[70],"parameter":[73],"derived":[75],"search":[78],"direction.":[79],"numerical":[81],"results":[82],"indicative":[84],"stability,":[87],"efficiency,":[88],"speed":[90],"algorithm,":[94],"based":[95],"on":[96],"performance":[97],"profiles":[98],"provided":[99],"by":[100],"Dolan":[101],"More.":[103]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
