{"id":"https://openalex.org/W4389236731","doi":"https://doi.org/10.1134/s0361768823060063","title":"Gradient-Free Algorithms for Solving Stochastic Saddle Optimization Problems with the Polyak\u2013\u0141ojasiewicz Condition","display_name":"Gradient-Free Algorithms for Solving Stochastic Saddle Optimization Problems with the Polyak\u2013\u0141ojasiewicz Condition","publication_year":2023,"publication_date":"2023-12-01","ids":{"openalex":"https://openalex.org/W4389236731","doi":"https://doi.org/10.1134/s0361768823060063"},"language":"en","primary_location":{"id":"doi:10.1134/s0361768823060063","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0361768823060063","pdf_url":null,"source":{"id":"https://openalex.org/S150218641","display_name":"Programming and Computer Software","issn_l":"0361-7688","issn":["0361-7688","1608-3261"],"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":"Programming and Computer Software","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/A5027087069","display_name":"S. I. Sadykov","orcid":"https://orcid.org/0009-0008-7101-6532"},"institutions":[{"id":"https://openalex.org/I153845743","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322","country_code":"RU","type":"education","lineage":["https://openalex.org/I153845743"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"S. I. Sadykov","raw_affiliation_strings":["Moscow Institute of Physics and Technology, Institutskii per. 9, 141701, Dolgoprudny, Russia"],"affiliations":[{"raw_affiliation_string":"Moscow Institute of Physics and Technology, Institutskii per. 9, 141701, Dolgoprudny, Russia","institution_ids":["https://openalex.org/I153845743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033385537","display_name":"A. V. Lobanov","orcid":"https://orcid.org/0000-0003-1620-9581"},"institutions":[{"id":"https://openalex.org/I153845743","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322","country_code":"RU","type":"education","lineage":["https://openalex.org/I153845743"]},{"id":"https://openalex.org/I4210101868","display_name":"Institute for System Programming","ror":"https://ror.org/017ef8252","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210101868","https://openalex.org/I4210124601"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"A. V. Lobanov","raw_affiliation_strings":["Moscow Institute of Physics and Technology, Institutskii per. 9, 141701, Dolgoprudny, Russia","Trusted Artificial Intelligence Research Center of the Ivannikov Institute for System Programming, Russian Academy of Sciences, ul. Solzhenitsyna 25, 109004, Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Moscow Institute of Physics and Technology, Institutskii per. 9, 141701, Dolgoprudny, Russia","institution_ids":["https://openalex.org/I153845743"]},{"raw_affiliation_string":"Trusted Artificial Intelligence Research Center of the Ivannikov Institute for System Programming, Russian Academy of Sciences, ul. Solzhenitsyna 25, 109004, Moscow, Russia","institution_ids":["https://openalex.org/I4210101868"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083898614","display_name":"\u0410. \u041c. \u0420\u0430\u0439\u0433\u043e\u0440\u043e\u0434\u0441\u043a\u0438\u0439","orcid":"https://orcid.org/0000-0001-8614-9612"},"institutions":[{"id":"https://openalex.org/I135226738","display_name":"Adyghe State University","ror":"https://ror.org/00tf0yk25","country_code":"RU","type":"education","lineage":["https://openalex.org/I135226738"]},{"id":"https://openalex.org/I153845743","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322","country_code":"RU","type":"education","lineage":["https://openalex.org/I153845743"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"A. M. Raigorodskii","raw_affiliation_strings":["Caucasian Mathematical Center of the Adyghe State University, ul. Pervomaiskaya 208, 385000, Maykop, Russia","Moscow Institute of Physics and Technology, Institutskii per. 9, 141701, Dolgoprudny, Russia"],"affiliations":[{"raw_affiliation_string":"Caucasian Mathematical Center of the Adyghe State University, ul. Pervomaiskaya 208, 385000, Maykop, Russia","institution_ids":["https://openalex.org/I135226738"]},{"raw_affiliation_string":"Moscow Institute of Physics and Technology, Institutskii per. 9, 141701, Dolgoprudny, Russia","institution_ids":["https://openalex.org/I153845743"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5027087069"],"corresponding_institution_ids":["https://openalex.org/I153845743"],"apc_list":null,"apc_paid":null,"fwci":0.4331,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.58047707,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"49","issue":"6","first_page":"535","last_page":"547"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9951000213623047,"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/oracle","display_name":"Oracle","score":0.6977943181991577},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.6772065758705139},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5897138118743896},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5769370198249817},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5363266468048096},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.5165523290634155},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.5110870003700256},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4686051607131958},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4527192711830139},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4384611248970032},{"id":"https://openalex.org/keywords/stochastic-approximation","display_name":"Stochastic approximation","score":0.42950063943862915},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41983261704444885},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28433823585510254},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11260056495666504},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09158864617347717},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.09124577045440674}],"concepts":[{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.6977943181991577},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.6772065758705139},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5897138118743896},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5769370198249817},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5363266468048096},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.5165523290634155},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.5110870003700256},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4686051607131958},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4527192711830139},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4384611248970032},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.42950063943862915},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41983261704444885},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28433823585510254},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11260056495666504},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09158864617347717},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.09124577045440674},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"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/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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/s0361768823060063","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0361768823060063","pdf_url":null,"source":{"id":"https://openalex.org/S150218641","display_name":"Programming and Computer Software","issn_l":"0361-7688","issn":["0361-7688","1608-3261"],"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":"Programming and Computer Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.46000000834465027,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1981042292","https://openalex.org/W2021204697","https://openalex.org/W2026258334","https://openalex.org/W2294138114","https://openalex.org/W2767075075","https://openalex.org/W2775085189","https://openalex.org/W2963248893","https://openalex.org/W3134040152","https://openalex.org/W3176874790","https://openalex.org/W4320561688","https://openalex.org/W4379539282","https://openalex.org/W4396714658","https://openalex.org/W4399437736"],"related_works":["https://openalex.org/W4236459141","https://openalex.org/W4205304778","https://openalex.org/W2020252434","https://openalex.org/W73248859","https://openalex.org/W2584253892","https://openalex.org/W2350324449","https://openalex.org/W119381072","https://openalex.org/W2034033896","https://openalex.org/W2094891943","https://openalex.org/W4240399920"],"abstract_inverted_index":{"This":[0],"paper":[1],"focuses":[2],"on":[3,43,78],"solving":[4],"a":[5,15,45,79],"subclass":[6],"of":[7,67],"stochastic":[8,53],"nonconvex-nonconcave":[9],"black":[10],"box":[11],"optimization":[12],"problems":[13],"with":[14,84],"saddle":[16],"point":[17],"that":[18,61],"satisfy":[19],"the":[20,30,70],"Polyak\u2013\u0141ojasiewicz":[21],"(PL)":[22],"condition.":[23],"To":[24],"solve":[25],"this":[26],"problem,":[27],"we":[28],"provide":[29],"first":[31],"(to":[32],"our":[33],"best":[34],"knowledge)":[35],"gradient-free":[36],"algorithm.":[37,56],"The":[38,73],"proposed":[39],"approach":[40],"is":[41],"based":[42],"applying":[44],"gradient":[46,54],"approximation":[47],"(kernel":[48],"approximation)":[49],"to":[50,69],"an":[51,85],"oracle-biased":[52],"descent":[55],"We":[57],"present":[58],"theoretical":[59,74],"estimates":[60],"guarantee":[62],"its":[63],"global":[64],"linear":[65],"rate":[66],"convergence":[68],"desired":[71],"accuracy.":[72],"results":[75],"are":[76],"checked":[77],"model":[80],"example":[81],"by":[82],"comparison":[83],"algorithm":[86],"using":[87],"Gaussian":[88],"approximation.":[89]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-01-23T23:20:30.427331","created_date":"2025-10-10T00:00:00"}
