{"id":"https://openalex.org/W4389879357","doi":"https://doi.org/10.1134/s000511792308009x","title":"Generalization of the Carath\u00e9odory Theorem and the Maximum Principle in Averaged Problems of Non-Linear Programming","display_name":"Generalization of the Carath\u00e9odory Theorem and the Maximum Principle in Averaged Problems of Non-Linear Programming","publication_year":2023,"publication_date":"2023-08-01","ids":{"openalex":"https://openalex.org/W4389879357","doi":"https://doi.org/10.1134/s000511792308009x"},"language":"en","primary_location":{"id":"doi:10.1134/s000511792308009x","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1134/s000511792308009x","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/A5050782960","display_name":"\u0410. \u041c. \u0426\u0438\u0440\u043b\u0438\u043d","orcid":"https://orcid.org/0000-0002-3637-6160"},"institutions":[{"id":"https://openalex.org/I4210143630","display_name":"Program Systems Institute of RAS","ror":"https://ror.org/040r4cv22","country_code":"RU","type":"education","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210143630"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"A. M. Tsirlin","raw_affiliation_strings":["Ailamazyan Program Systems Institute, Russian Academy of Sciences, Pereslavl-Zalessky, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ailamazyan Program Systems Institute, Russian Academy of Sciences, Pereslavl-Zalessky, Russia","institution_ids":["https://openalex.org/I4210143630"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050782960"],"corresponding_institution_ids":["https://openalex.org/I4210143630"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17511325,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"84","issue":"8","first_page":"840","last_page":"847"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13020","display_name":"Heat Transfer and Mathematical Modeling","score":0.8730000257492065,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13020","display_name":"Heat Transfer and Mathematical Modeling","score":0.8730000257492065,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14512","display_name":"Technology and Human Factors in Education and Health","score":0.8402000069618225,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T14294","display_name":"Impulse Buying and Technology Impacts","score":0.8356999754905701,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8919799327850342},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.7227699756622314},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5622109770774841},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5530692338943481},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5082396864891052},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4594297409057617},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4332120716571808},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4163571894168854},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3969077169895172},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3826930522918701}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8919799327850342},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7227699756622314},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5622109770774841},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5530692338943481},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5082396864891052},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4594297409057617},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4332120716571808},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4163571894168854},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3969077169895172},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3826930522918701},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s000511792308009x","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1134/s000511792308009x","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":1,"referenced_works":["https://openalex.org/W2011026422"],"related_works":["https://openalex.org/W3182827720","https://openalex.org/W1596838019","https://openalex.org/W2133947431","https://openalex.org/W2490196280","https://openalex.org/W3208509670","https://openalex.org/W2100864966","https://openalex.org/W2109304297","https://openalex.org/W3173321515","https://openalex.org/W2988866178","https://openalex.org/W2083709218"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"relationship":[2],"between":[3],"the":[4,14,19,28,35,42,51,58,61,69,104,110,114],"averaging":[5,12,36,99],"of":[6,16,18,32,37,41,45,60,79,85,103,113],"functions":[7,38,40,107],"over":[8,13,100],"time":[9,70],"and":[10,30,64,106],"its":[11],"set":[15],"values":[17,44,112],"required":[20],"variables":[21,105],"is":[22,48,72,88],"considered.":[23],"Optimization":[24],"problems":[25,56,97],"are":[26,92],"studied,":[27],"criterion":[29],"constraints":[31],"which":[33],"include":[34],"or":[39],"average":[43,111],"variables.":[46,115],"It":[47],"shown":[49],"that":[50],"optimality":[52],"conditions":[53,91],"for":[54,94],"these":[55],"have":[57],"form":[59],"maximum":[62],"principle,":[63],"their":[65],"optimal":[66],"solution":[67],"in":[68],"domain":[71],"a":[73,86,101],"piecewise":[74],"constant":[75],"function.":[76],"A":[77],"generalization":[78],"Carath\u00e9odory\u2019s":[80],"theorem":[81],"on":[82,109],"convex":[83],"hulls":[84],"function":[87],"proved.":[89],"Optimality":[90],"obtained":[93],"non-linear":[95],"programming":[96],"with":[98],"part":[102],"depending":[108]},"counts_by_year":[],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}
