{"id":"https://openalex.org/W2739392069","doi":"https://doi.org/10.1051/ro/2017057","title":"An adaptive nonmonotone trust region method based on a modified scalar approximation of the Hessian in the successive quadratic subproblems","display_name":"An adaptive nonmonotone trust region method based on a modified scalar approximation of the Hessian in the successive quadratic subproblems","publication_year":2017,"publication_date":"2017-07-25","ids":{"openalex":"https://openalex.org/W2739392069","doi":"https://doi.org/10.1051/ro/2017057","mag":"2739392069"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2017057","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2017057","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040978431","display_name":"Saeed Rezaee","orcid":"https://orcid.org/0000-0002-2636-3868"},"institutions":[{"id":"https://openalex.org/I928334797","display_name":"Semnan University","ror":"https://ror.org/029gksw03","country_code":"IR","type":"education","lineage":["https://openalex.org/I928334797"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Saeed Rezaee","raw_affiliation_strings":["Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, P.O. Box: 35195\u2013363, Semnan, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, P.O. Box: 35195\u2013363, Semnan, Iran","institution_ids":["https://openalex.org/I928334797"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091349408","display_name":"Saman Babaie\u2013Kafaki","orcid":"https://orcid.org/0000-0003-0122-8384"},"institutions":[{"id":"https://openalex.org/I928334797","display_name":"Semnan University","ror":"https://ror.org/029gksw03","country_code":"IR","type":"education","lineage":["https://openalex.org/I928334797"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Saman Babaie-Kafaki","raw_affiliation_strings":["Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, P.O. Box: 35195\u2013363, Semnan, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, P.O. Box: 35195\u2013363, Semnan, Iran","institution_ids":["https://openalex.org/I928334797"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5091349408"],"corresponding_institution_ids":["https://openalex.org/I928334797"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.14112704,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"53","issue":"3","first_page":"829","last_page":"839"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9864000082015991,"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":0.9861000180244446,"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/hessian-matrix","display_name":"Hessian matrix","score":0.9563755989074707},{"id":"https://openalex.org/keywords/trust-region","display_name":"Trust region","score":0.8527840375900269},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.7396919131278992},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.6665794849395752},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.645027756690979},{"id":"https://openalex.org/keywords/quadratic-model","display_name":"Quadratic model","score":0.5239053964614868},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5139829516410828},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4741867482662201},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46015647053718567},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.43975698947906494},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25700098276138306},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.050529658794403076}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.9563755989074707},{"id":"https://openalex.org/C89109886","wikidata":"https://www.wikidata.org/wiki/Q1535924","display_name":"Trust region","level":3,"score":0.8527840375900269},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.7396919131278992},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.6665794849395752},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.645027756690979},{"id":"https://openalex.org/C2983524802","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic model","level":3,"score":0.5239053964614868},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5139829516410828},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4741867482662201},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46015647053718567},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.43975698947906494},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25700098276138306},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.050529658794403076},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C150077022","wikidata":"https://www.wikidata.org/wiki/Q3136137","display_name":"Response surface methodology","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1051/ro/2017057","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2017057","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:numdam.org:RO_2019__53_3_829_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ro/2017057/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"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":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W613054787","https://openalex.org/W1581667416","https://openalex.org/W1857781112","https://openalex.org/W1968410008","https://openalex.org/W1977109023","https://openalex.org/W2006468116","https://openalex.org/W2009941369","https://openalex.org/W2012766316","https://openalex.org/W2016518303","https://openalex.org/W2042877555","https://openalex.org/W2043701472","https://openalex.org/W2047785690","https://openalex.org/W2061054410","https://openalex.org/W2062145486","https://openalex.org/W2064217481","https://openalex.org/W2066205820","https://openalex.org/W2070617022","https://openalex.org/W2076605490","https://openalex.org/W2078029965","https://openalex.org/W2085137170","https://openalex.org/W2085814643","https://openalex.org/W2095133175","https://openalex.org/W2149454052","https://openalex.org/W2156005216","https://openalex.org/W3175721619"],"related_works":["https://openalex.org/W2115477667","https://openalex.org/W2352811179","https://openalex.org/W2373906883","https://openalex.org/W633727474","https://openalex.org/W2089168582","https://openalex.org/W2026387094","https://openalex.org/W1989684674","https://openalex.org/W2122918402","https://openalex.org/W2356599694","https://openalex.org/W2739392069"],"abstract_inverted_index":{"Based":[0],"on":[1,57],"a":[2,8,32,58],"modified":[3],"secant":[4],"equation,":[5],"we":[6,23],"propose":[7],"scalar":[9],"approximation":[10],"of":[11,60,65,77],"the":[12,18,44,66,70,78],"Hessian":[13],"to":[14],"be":[15],"used":[16],"in":[17],"trust":[19,28],"region":[20,29],"subproblem.":[21],"Then,":[22],"suggest":[24],"an":[25],"adaptive":[26],"nonmonotone":[27],"algorithm":[30,46],"with":[31],"simple":[33],"quadratic":[34],"model.":[35],"Under":[36],"proper":[37],"conditions,":[38],"it":[39],"is":[40,47],"briefly":[41],"shown":[42],"that":[43],"proposed":[45,79],"globally":[48],"and":[49],"locally":[50],"superlinearly":[51],"convergent.":[52],"Numerical":[53],"experiments":[54],"are":[55],"done":[56],"set":[59],"unconstrained":[61],"optimization":[62],"test":[63],"problems":[64],"CUTEr":[67],"collection,":[68],"using":[69],"Dolan-Mor\u00e9":[71],"performance":[72],"profile.":[73],"They":[74],"demonstrate":[75],"efficiency":[76],"algorithm.":[80]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-07T06:14:10.401900","created_date":"2025-10-10T00:00:00"}