{"id":"https://openalex.org/W3092479710","doi":"https://doi.org/10.1007/s10107-021-01727-x","title":"Inexact accelerated high-order proximal-point methods","display_name":"Inexact accelerated high-order proximal-point methods","publication_year":2021,"publication_date":"2021-11-11","ids":{"openalex":"https://openalex.org/W3092479710","doi":"https://doi.org/10.1007/s10107-021-01727-x","mag":"3092479710"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-021-01727-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-021-01727-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-021-01727-x.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10107-021-01727-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067792459","display_name":"Yurii Nesterov","orcid":"https://orcid.org/0000-0002-0542-8757"},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Yurii Nesterov","raw_affiliation_strings":["Center for Operations Research and Econometrics (CORE), Catholic University of Louvain (UCL), Louvain-la-Neuve, Belgium"],"affiliations":[{"raw_affiliation_string":"Center for Operations Research and Econometrics (CORE), Catholic University of Louvain (UCL), Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5067792459"],"corresponding_institution_ids":["https://openalex.org/I95674353"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2890},"fwci":3.7371,"has_fulltext":true,"cited_by_count":38,"citation_normalized_percentile":{"value":0.93769237,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"197","issue":"1","first_page":"1","last_page":"26"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9993000030517578,"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":0.9990000128746033,"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/algorithm","display_name":"Algorithm","score":0.713045597076416},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4536615312099457}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.713045597076416},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4536615312099457}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10107-021-01727-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-021-01727-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-021-01727-x.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03324460v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03324460","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"[Research Report] Center for Operations Research and Econometrics (CORE). 2021","raw_type":"Reports"},{"id":"pmh:oai:RePEc:cor:louvrp:3252","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"preprint"},{"id":"pmh:oai:dial.uclouvain.be:boreal:227219","is_oa":true,"landing_page_url":"http://hdl.handle.net/2078.1/227219","pdf_url":null,"source":{"id":"https://openalex.org/S4306401902","display_name":"Digital Access to Libraries (Universit\u00e9 catholique de Louvain (UCL), l'Universit\u00e9 de Namur (UNamur) and the Universit\u00e9 Saint-Louis (USL-B))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I95674353","host_organization_name":"UCLouvain","host_organization_lineage":["https://openalex.org/I95674353"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/workingPaper"},{"id":"pmh:oai:dial.uclouvain.be:boreal:277134","is_oa":true,"landing_page_url":"http://hdl.handle.net/2078.1/277134","pdf_url":null,"source":{"id":"https://openalex.org/S4306401902","display_name":"Digital Access to Libraries (Universit\u00e9 catholique de Louvain (UCL), l'Universit\u00e9 de Namur (UNamur) and the Universit\u00e9 Saint-Louis (USL-B))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I95674353","host_organization_name":"UCLouvain","host_organization_lineage":["https://openalex.org/I95674353"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical programming, Vol. 197, no.1, p. 1-26 (2023)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s10107-021-01727-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-021-01727-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-021-01727-x.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1041279674","display_name":null,"funder_award_id":"ANR-19-P3IA-0003","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2092057362","display_name":null,"funder_award_id":"19-P3IA-0003","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2103506358","display_name":null,"funder_award_id":"(ANR-19-P3IA-0003)","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G30976567","display_name":null,"funder_award_id":"MIAI@Grenoble Alpes (ANR-19-P3IA-0003)","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3104333717","display_name":null,"funder_award_id":"MIAI@Grenoble Alpes","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3680960908","display_name":null,"funder_award_id":"ANR-19-P3IA-000","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4023648257","display_name":"ACelerated COnvex OPTimization","funder_award_id":"788368","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4690472590","display_name":null,"funder_award_id":"788368","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G4956428346","display_name":null,"funder_award_id":"Horizon 2020 research and innovatio","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5036817778","display_name":null,"funder_award_id":"European Union's Horizon 2020 research and innov","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G6851345361","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8051717526","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8318064016","display_name":null,"funder_award_id":"Horizon","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8318455765","display_name":null,"funder_award_id":"ANR-19","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8633428685","display_name":null,"funder_award_id":"European Union's Horizon 2020 research and innovat","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3092479710.pdf","grobid_xml":"https://content.openalex.org/works/W3092479710.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W181062240","https://openalex.org/W1632601927","https://openalex.org/W1953936588","https://openalex.org/W1977109023","https://openalex.org/W2009274429","https://openalex.org/W2032690622","https://openalex.org/W2037679050","https://openalex.org/W2038497950","https://openalex.org/W2043674215","https://openalex.org/W2135779729","https://openalex.org/W2510806995","https://openalex.org/W2535496140","https://openalex.org/W2546420264","https://openalex.org/W2551153860","https://openalex.org/W2587712072","https://openalex.org/W2619885667","https://openalex.org/W2766175844","https://openalex.org/W2808862920","https://openalex.org/W2901838001","https://openalex.org/W2904609734","https://openalex.org/W2907917442","https://openalex.org/W2913535645","https://openalex.org/W2962824898","https://openalex.org/W2964511245","https://openalex.org/W2969945254","https://openalex.org/W3092425772","https://openalex.org/W3112051302","https://openalex.org/W3212136124","https://openalex.org/W6601205648"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2350741829","https://openalex.org/W2530322880"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,107],"paper,":[3],"we":[4,43,73],"present":[5,121],"a":[6,56,75],"new":[7,76,122],"framework":[8],"of":[9,15,25,33,66,104,109,134,152,162],"bi-level":[10],"unconstrained":[11],"minimization":[12],"for":[13,58,106],"development":[14],"accelerated":[16],"methods":[17,22,61,123],"in":[18,49],"Convex":[19],"Programming.":[20],"These":[21],"use":[23,45],"approximations":[24],"the":[26,51,59,67,80,92,100,125,132,150,153],"high-order":[27],"proximal":[28,154],"points,":[29,42],"which":[30,130],"are":[31],"solutions":[32],"some":[34],"auxiliary":[35,127,157],"parametric":[36],"optimization":[37],"problems.":[38],"For":[39],"computing":[40],"these":[41,163],"can":[44],"different":[46],"methods,":[47,110],"and,":[48],"particular,":[50],"lower-order":[52],"schemes.":[53],"This":[54,95],"opens":[55],"possibility":[57],"latter":[60],"to":[62,113],"overpass":[63],"traditional":[64],"limits":[65],"Complexity":[68],"Theory.":[69],"As":[70],"an":[71],"example,":[72],"obtain":[74],"second-order":[77],"method":[78],"with":[79,115,124],"convergence":[81,105,135],"rate":[82,96,103,133],"$$O\\left(":[83,136],"k^{-4}\\right)":[84],"$$":[85,139],"<mml:math":[86,140,147],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>O</mml:mi><mml:mfenced><mml:msup><mml:mi>k</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mfenced></mml:mrow></mml:math>":[87],",":[88,142],"where":[89,143],"k":[90],"is":[91,97,149,165],"iteration":[93,161],"counter.":[94],"better":[98],"than":[99],"maximal":[101],"possible":[102],"type":[108],"as":[111],"applied":[112],"functions":[114],"Lipschitz":[116],"continuous":[117],"Hessian.":[118],"We":[119],"also":[120],"exact":[126],"search":[128],"procedure,":[129],"have":[131],"k^{-(3p+1)/":[137],"2}\\right)":[138],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>O</mml:mi><mml:mfenced><mml:msup><mml:mi>k</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mi>p</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mfenced></mml:mrow></mml:math>":[141],"$$p":[144],"\\ge":[145],"1$$":[146],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>\u2265</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>":[148],"order":[151],"operator.":[155],"The":[156],"problem":[158],"at":[159],"each":[160],"schemes":[164],"convex.":[166]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}