{"id":"https://openalex.org/W2926844976","doi":"https://doi.org/10.1134/s0005117919010090","title":"On the Properties of the Method of Minimization for Convex Functions with Relaxation on the Distance to Extremum","display_name":"On the Properties of the Method of Minimization for Convex Functions with Relaxation on the Distance to Extremum","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2926844976","doi":"https://doi.org/10.1134/s0005117919010090","mag":"2926844976"},"language":"en","primary_location":{"id":"doi:10.1134/s0005117919010090","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0005117919010090","pdf_url":null,"source":{"id":"https://openalex.org/S134188425","display_name":"Automation and Remote Control","issn_l":"0005-1179","issn":["0005-1179","1608-3032"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automation and Remote Control","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/A5088654072","display_name":"V. N. Krutikov","orcid":"https://orcid.org/0000-0001-8704-1670"},"institutions":[{"id":"https://openalex.org/I52135307","display_name":"Kemerovo State University","ror":"https://ror.org/036yvre49","country_code":"RU","type":"education","lineage":["https://openalex.org/I52135307"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"V. N. Krutikov","raw_affiliation_strings":["Kemerovo State University, Kemerovo, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kemerovo State University, Kemerovo, Russia","institution_ids":["https://openalex.org/I52135307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074318154","display_name":"Nikita S. Samoilenko","orcid":null},"institutions":[{"id":"https://openalex.org/I52135307","display_name":"Kemerovo State University","ror":"https://ror.org/036yvre49","country_code":"RU","type":"education","lineage":["https://openalex.org/I52135307"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"N. S. Samoilenko","raw_affiliation_strings":["Kemerovo State University, Kemerovo, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kemerovo State University, Kemerovo, Russia","institution_ids":["https://openalex.org/I52135307"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005210912","display_name":"\u0412\u043b\u0430\u0434\u0438\u043c\u0438\u0440 \u0412\u0438\u043a\u0442\u043e\u0440\u043e\u0432\u0438\u0447 \u041c\u0435\u0448\u0435\u0447\u043a\u0438\u043d","orcid":null},"institutions":[{"id":"https://openalex.org/I52135307","display_name":"Kemerovo State University","ror":"https://ror.org/036yvre49","country_code":"RU","type":"education","lineage":["https://openalex.org/I52135307"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"V. V. Meshechkin","raw_affiliation_strings":["Kemerovo State University, Kemerovo, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kemerovo State University, Kemerovo, Russia","institution_ids":["https://openalex.org/I52135307"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5088654072"],"corresponding_institution_ids":["https://openalex.org/I52135307"],"apc_list":null,"apc_paid":null,"fwci":1.5757,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.80846008,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"80","issue":"1","first_page":"102","last_page":"111"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.998199999332428,"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":0.998199999332428,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9847999811172485,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.982200026512146,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/subgradient-method","display_name":"Subgradient method","score":0.8159402012825012},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7855372428894043},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6206296682357788},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.6152790784835815},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5513958930969238},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5450218319892883},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5356513857841492},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5162484645843506},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5023727416992188},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49507012963294983},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.49462005496025085},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.43970152735710144},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.4368986487388611},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4368543028831482},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41607123613357544},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.38226598501205444},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2823235094547272},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15464147925376892},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.13084805011749268},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09166911244392395}],"concepts":[{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.8159402012825012},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7855372428894043},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6206296682357788},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.6152790784835815},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5513958930969238},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5450218319892883},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5356513857841492},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5162484645843506},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5023727416992188},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49507012963294983},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.49462005496025085},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.43970152735710144},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.4368986487388611},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4368543028831482},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41607123613357544},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.38226598501205444},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2823235094547272},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15464147925376892},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.13084805011749268},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09166911244392395},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s0005117919010090","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0005117919010090","pdf_url":null,"source":{"id":"https://openalex.org/S134188425","display_name":"Automation and Remote Control","issn_l":"0005-1179","issn":["0005-1179","1608-3032"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automation and Remote Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W11112849","https://openalex.org/W224775207","https://openalex.org/W1985240368","https://openalex.org/W2008571296","https://openalex.org/W2036591726","https://openalex.org/W2129470876","https://openalex.org/W2167732364","https://openalex.org/W2790570656","https://openalex.org/W4240463582"],"related_works":["https://openalex.org/W2128927076","https://openalex.org/W2465405765","https://openalex.org/W4297153560","https://openalex.org/W2964186284","https://openalex.org/W2804400349","https://openalex.org/W2140018151","https://openalex.org/W3084689723","https://openalex.org/W3161275408","https://openalex.org/W3088056528","https://openalex.org/W2811183536"],"abstract_inverted_index":{"We":[0,85,112,129],"present":[1],"a":[2,33,126],"subgradient":[3],"method":[4,10,43,90],"of":[5,11,17,36,44,53,56,61,82,88,97,99,118,125,135],"minimization,":[6],"similar":[7],"to":[8,64,91],"the":[9,22,40,54,62,71,78,83,92,95,100,123,132],"minimal":[12],"iterations":[13],"for":[14,32,138],"solving":[15,139],"systems":[16],"equations,":[18],"which":[19],"inherits":[20],"from":[21],"latter":[23],"convergence":[24,107],"properties":[25],"on":[26,77,94,105,109,115],"quadratic":[27],"functions.":[28,111],"The":[29],"proposed":[30],"algorithm,":[31],"certain":[34],"set":[35],"parameters,":[37],"coincides":[38],"with":[39,59,141],"previously":[41],"known":[42],"minimizing":[45],"piecewise":[46],"linear":[47],"functions":[48,119],"and":[49,102],"is":[50,74],"an":[51],"element":[52],"family":[55],"minimization":[57],"methods":[58],"relaxation":[60],"distance":[63],"extremum,":[65],"developed":[66],"by":[67],"B.T.":[68],"Polyak,":[69],"where":[70],"step":[72],"length":[73],"calculated":[75],"based":[76],"predefined":[79],"minimum":[80],"value":[81],"function.":[84],"link":[86],"parameters":[87],"this":[89,136],"constraint":[93],"degree":[96],"homogeneity":[98],"function":[101],"obtain":[103],"estimates":[104],"its":[106],"rate":[108,124],"convex":[110],"prove":[113],"that":[114],"some":[116],"classes":[117],"it":[120],"converges":[121],"at":[122],"geometric":[127],"progression.":[128],"also":[130],"discuss":[131],"computational":[133],"capabilities":[134],"approach":[137],"problems":[140],"high":[142],"dimension.":[143]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
