{"id":"https://openalex.org/W2999153233","doi":"https://doi.org/10.1137/19m1259432","title":"Tensor Methods for Minimizing Convex Functions with H\u00f6lder Continuous Higher-Order Derivatives","display_name":"Tensor Methods for Minimizing Convex Functions with H\u00f6lder Continuous Higher-Order Derivatives","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2999153233","doi":"https://doi.org/10.1137/19m1259432","mag":"2999153233"},"language":"en","primary_location":{"id":"doi:10.1137/19m1259432","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1259432","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/19M1259432","source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/19M1259432","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"G. N. Grapiglia","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"G. N. Grapiglia","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Yu. Nesterov","orcid":"https://orcid.org/0000-0002-0542-8757"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yu. Nesterov","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8345,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.84956843,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"30","issue":"4","first_page":"2750","last_page":"2779"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.40299999713897705,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T12303","display_name":"Tensor decomposition and applications","score":0.40299999713897705,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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":0.28380000591278076,"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":0.11420000344514847,"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/tensor","display_name":"Tensor (intrinsic definition)","score":0.5539000034332275},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5266000032424927},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5058000087738037},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4862000048160553},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.48249998688697815},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.47859999537467957},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4668999910354614},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.43650001287460327}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8337000012397766},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5539000034332275},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5266000032424927},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5058000087738037},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4862000048160553},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.48249998688697815},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.47859999537467957},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4668999910354614},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.43650001287460327},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42089998722076416},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.38940000534057617},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3734000027179718},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3546999990940094},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34869998693466187},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.3294000029563904},{"id":"https://openalex.org/C50862404","wikidata":"https://www.wikidata.org/wiki/Q3075259","display_name":"Proper convex function","level":5,"score":0.3237999975681305},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.29829999804496765},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.29750001430511475},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.28529998660087585},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.26579999923706055},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2547999918460846}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/19m1259432","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1259432","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/19M1259432","source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1904.12559","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1904.12559","pdf_url":"https://arxiv.org/pdf/1904.12559","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:dial.uclouvain.be:boreal:223952","is_oa":true,"landing_page_url":"http://hdl.handle.net/2078.1/223952","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":"SIAM Journal on Optimization, Vol. 30, no. 4, p. 2750-2779 (2020)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1137/19m1259432","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1259432","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/19M1259432","source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3774921934","display_name":null,"funder_award_id":"406269/2016-5","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"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/G5433969572","display_name":null,"funder_award_id":"401288/2014-5","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"}],"funders":[{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2999153233.pdf","grobid_xml":"https://content.openalex.org/works/W2999153233.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W802720919","https://openalex.org/W2009941369","https://openalex.org/W2012604196","https://openalex.org/W2026890617","https://openalex.org/W2510806995","https://openalex.org/W2599851351","https://openalex.org/W2774800844","https://openalex.org/W2792215433","https://openalex.org/W2925648101","https://openalex.org/W2962824898","https://openalex.org/W3021249612"],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1,104],"paper":[2],"we":[3,38,61,82],"study":[4],"$p$-order":[5],"methods":[6],"for":[7,45,69,103],"unconstrained":[8],"minimization":[9],"of":[10,43,67,92,98],"convex":[11],"functions":[12],"that":[13,57],"are":[14],"$p$-times":[15],"differentiable":[16],"$(p":[17],"\u2265":[18],"2)$":[19],"with":[20,29,89],"$\\\\nu$-H\u00f6lder":[21],"continuous":[22],"$p$th":[23],"derivatives.":[24],"We":[25],"propose":[26],"tensor":[27,87],"schemes":[28,35],"and":[30],"without":[31,36],"acceleration.":[32],"For":[33,74],"the":[34,47,70,75],"acceleration,":[37],"establish":[39],"iteration":[40,90],"complexity":[41,65,91,96],"bounds":[42],"${\\\\Os}(\\\\epsilon^{-1/(p+\\\\nu-1)})$":[44],"reducing":[46],"functional":[48],"residual":[49],"below":[50],"a":[51,84],"given":[52],"$\\\\epsilon":[53],"\\\\in":[54],"(0,1)$.":[55],"Assuming":[56],"$\\\\nu$":[58,79],"is":[59,80,100],"known,":[60],"obtain":[62],"an":[63],"improved":[64],"bound":[66,97],"${\\\\Os}(\\\\epsilon^{-1/(p+\\\\nu)})$":[68],"corresponding":[71],"accelerated":[72,86],"scheme.":[73],"case":[76],"in":[77],"which":[78],"unknown,":[81],"present":[83],"universal":[85],"scheme":[88],"${\\\\Os}(\\\\epsilon^{-p/[(p+1)(p+\\\\nu-1)]})$.":[93],"A":[94],"lower":[95],"${\\\\Os}(\\\\epsilon^{-2/[3(p+\\\\nu)-2])$":[99],"also":[101],"obtained":[102],"problem":[105],"class.":[106]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2020-01-23T00:00:00"}