{"id":"https://openalex.org/W2969652412","doi":"https://doi.org/10.1080/10556788.2019.1653868","title":"Accelerated multiple step-size methods for solving unconstrained optimization problems","display_name":"Accelerated multiple step-size methods for solving unconstrained optimization problems","publication_year":2019,"publication_date":"2019-08-22","ids":{"openalex":"https://openalex.org/W2969652412","doi":"https://doi.org/10.1080/10556788.2019.1653868","mag":"2969652412"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2019.1653868","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2019.1653868","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://figshare.com/articles/Accelerated_multiple_step-size_methods_for_solving_unconstrained_optimization_problems/9722189","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090875151","display_name":"Branislav Ivanov","orcid":"https://orcid.org/0000-0001-9179-0965"},"institutions":[{"id":"https://openalex.org/I4068193","display_name":"University of Belgrade","ror":"https://ror.org/02qsmb048","country_code":"RS","type":"education","lineage":["https://openalex.org/I4068193"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Branislav Ivanov","raw_affiliation_strings":["Technical Faculty in Bor, University of Belgrade, Bor, Serbia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technical Faculty in Bor, University of Belgrade, Bor, Serbia","institution_ids":["https://openalex.org/I4068193"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038736735","display_name":"Predrag S. Stanimirovi\u0107","orcid":"https://orcid.org/0000-0003-0655-3741"},"institutions":[{"id":"https://openalex.org/I152518017","display_name":"University of Nis","ror":"https://ror.org/00965bg92","country_code":"RS","type":"education","lineage":["https://openalex.org/I152518017"]}],"countries":["RS"],"is_corresponding":true,"raw_author_name":"Predrag S. Stanimirovi\u0107","raw_affiliation_strings":["Faculty of Sciences and Mathematics, University of Ni\u0161, Ni\u0161, Serbia"],"raw_orcid":"https://orcid.org/0000-0003-0655-3741","affiliations":[{"raw_affiliation_string":"Faculty of Sciences and Mathematics, University of Ni\u0161, Ni\u0161, Serbia","institution_ids":["https://openalex.org/I152518017"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034541132","display_name":"Gradimir V. Milovanovi\u0107","orcid":"https://orcid.org/0000-0002-3255-8127"},"institutions":[{"id":"https://openalex.org/I1338511612","display_name":"Serbian Academy of Sciences and Arts","ror":"https://ror.org/05m1y4204","country_code":"RS","type":"government","lineage":["https://openalex.org/I1338511612"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Gradimir V. Milovanovi\u0107","raw_affiliation_strings":["Serbian Academy of Sciences and Arts, Belgrade, Serbia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Serbian Academy of Sciences and Arts, Belgrade, Serbia","institution_ids":["https://openalex.org/I1338511612"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027662639","display_name":"Sne\u017eana Djordjevi\u0107","orcid":null},"institutions":[{"id":"https://openalex.org/I152518017","display_name":"University of Nis","ror":"https://ror.org/00965bg92","country_code":"RS","type":"education","lineage":["https://openalex.org/I152518017"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Sne\u017eana Djordjevi\u0107","raw_affiliation_strings":["Faculty of Technology, University of Ni\u0161, Ni\u0161, Serbia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Technology, University of Ni\u0161, Ni\u0161, Serbia","institution_ids":["https://openalex.org/I152518017"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084650057","display_name":"Ivona Brajevi\u0107","orcid":"https://orcid.org/0000-0002-2999-3187"},"institutions":[{"id":"https://openalex.org/I152518017","display_name":"University of Nis","ror":"https://ror.org/00965bg92","country_code":"RS","type":"education","lineage":["https://openalex.org/I152518017"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Ivona Brajevi\u0107","raw_affiliation_strings":["Faculty of Sciences and Mathematics, University of Ni\u0161, Ni\u0161, Serbia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Sciences and Mathematics, University of Ni\u0161, Ni\u0161, Serbia","institution_ids":["https://openalex.org/I152518017"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5038736735"],"corresponding_institution_ids":["https://openalex.org/I152518017"],"apc_list":null,"apc_paid":null,"fwci":1.2978,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.78978841,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"36","issue":"5","first_page":"998","last_page":"1029"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":1.0,"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":1.0,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9972000122070312,"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"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.995199978351593,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.830470085144043},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.6795777678489685},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.5607513785362244},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.546704113483429},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.529140293598175},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.5083834528923035},{"id":"https://openalex.org/keywords/newtons-method-in-optimization","display_name":"Newton's method in optimization","score":0.5042082071304321},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5036956667900085},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4863277077674866},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.4609646499156952},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4534109830856323},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.43011558055877686},{"id":"https://openalex.org/keywords/backtracking","display_name":"Backtracking","score":0.42841577529907227},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.4216662645339966},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.3784922957420349},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3659725785255432},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3523523807525635},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.2709818482398987},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1405724585056305},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.07388603687286377},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.06810632348060608}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.830470085144043},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.6795777678489685},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.5607513785362244},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.546704113483429},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.529140293598175},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.5083834528923035},{"id":"https://openalex.org/C179127668","wikidata":"https://www.wikidata.org/wiki/Q17086396","display_name":"Newton's method in optimization","level":4,"score":0.5042082071304321},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5036956667900085},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4863277077674866},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.4609646499156952},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4534109830856323},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.43011558055877686},{"id":"https://openalex.org/C156884757","wikidata":"https://www.wikidata.org/wiki/Q798554","display_name":"Backtracking","level":2,"score":0.42841577529907227},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.4216662645339966},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3784922957420349},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3659725785255432},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3523523807525635},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.2709818482398987},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1405724585056305},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.07388603687286377},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.06810632348060608},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/10556788.2019.1653868","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2019.1653868","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},{"id":"pmh:oai:figshare.com:article/9722189","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Accelerated_multiple_step-size_methods_for_solving_unconstrained_optimization_problems/9722189","pdf_url":"https://figshare.com/articles/Accelerated_multiple_step-size_methods_for_solving_unconstrained_optimization_problems/9722189","source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":"Text"},{"id":"doi:10.6084/m9.figshare.9722189.v1","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.9722189.v1","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/9722189","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Accelerated_multiple_step-size_methods_for_solving_unconstrained_optimization_problems/9722189","pdf_url":"https://figshare.com/articles/Accelerated_multiple_step-size_methods_for_solving_unconstrained_optimization_problems/9722189","source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334771","display_name":"Science and Engineering Research Board","ror":"https://ror.org/03ffdsr55"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2969652412.pdf","grobid_xml":"https://content.openalex.org/works/W2969652412.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W613054787","https://openalex.org/W1497566274","https://openalex.org/W1530695493","https://openalex.org/W1676543742","https://openalex.org/W1981917775","https://openalex.org/W1989566487","https://openalex.org/W2010210703","https://openalex.org/W2012341322","https://openalex.org/W2014424370","https://openalex.org/W2023358569","https://openalex.org/W2023440361","https://openalex.org/W2039771911","https://openalex.org/W2044934031","https://openalex.org/W2045806169","https://openalex.org/W2050096287","https://openalex.org/W2069435104","https://openalex.org/W2076605490","https://openalex.org/W2081842231","https://openalex.org/W2097593805","https://openalex.org/W2099607078","https://openalex.org/W2149454052","https://openalex.org/W2326893138","https://openalex.org/W2412011269","https://openalex.org/W2492617191","https://openalex.org/W2738079818","https://openalex.org/W2781207057","https://openalex.org/W2886287668","https://openalex.org/W2899960592","https://openalex.org/W4249667877","https://openalex.org/W4293775970","https://openalex.org/W6601250092"],"related_works":["https://openalex.org/W2349115186","https://openalex.org/W2094175538","https://openalex.org/W937190428","https://openalex.org/W2959000961","https://openalex.org/W2378491594","https://openalex.org/W2938193256","https://openalex.org/W2355152789","https://openalex.org/W2349550263","https://openalex.org/W2976230624","https://openalex.org/W1984402599"],"abstract_inverted_index":{"Two":[0],"transformations":[1],"of":[2,26,48,119,131,145,153],"gradient-descent":[3,32,49,62],"iterative":[4,55],"methods":[5,50,63,78,122,128],"for":[6,64,82],"solving":[7,65],"unconstrained":[8,66],"optimization":[9,67],"are":[10,69,79],"proposed.":[11],"The":[12,34,76],"first":[13],"transformation":[14,36],"is":[15,20,37,43,96,112],"called":[16],"modification":[17],"and":[18,41,73,134,150],"it":[19,42],"defined":[21,44],"using":[22],"a":[23,46,58],"small":[24],"enlargement":[25],"the":[27,52,90,93,99,105,120,132,147,151],"step":[28,94],"size":[29,95],"in":[30,129],"various":[31],"methods.":[33],"second":[35],"termed":[38],"as":[39,45],"hybridization":[40],"composition":[47],"with":[51,123,138],"Picard\u2013Mann":[53],"hybrid":[54],"process.":[56],"As":[57],"result,":[59],"several":[60],"accelerated":[61],"problems":[68],"presented,":[70],"investigated":[71],"theoretically":[72],"numerically":[74],"compared.":[75],"proposed":[77,121],"globally":[80],"convergent":[81],"uniformly":[83],"convex":[84,109],"functions":[85,111],"satisfying":[86],"certain":[87],"condition":[88],"under":[89],"assumption":[91],"that":[92],"determined":[97],"by":[98],"backtracking":[100],"line":[101],"search.":[102],"In":[103],"addition,":[104],"convergence":[106],"on":[107],"strictly":[108],"quadratic":[110],"discussed.":[113],"Numerical":[114],"comparisons":[115],"show":[116],"better":[117],"behaviour":[118],"respect":[124,139],"to":[125,140],"some":[126],"existing":[127],"view":[130],"Dolan":[133],"Mor\u00e9's":[135],"performance":[136],"profile":[137],"all":[141],"analysed":[142],"characteristics:":[143],"number":[144,152],"iterations,":[146],"CPU":[148],"time,":[149],"function":[154],"evaluations.":[155]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}