{"id":"https://openalex.org/W4383618801","doi":"https://doi.org/10.1007/s10957-023-02261-w","title":"Iteration Complexity of Fixed-Step Methods by Nesterov and Polyak for Convex Quadratic Functions","display_name":"Iteration Complexity of Fixed-Step Methods by Nesterov and Polyak for Convex Quadratic Functions","publication_year":2023,"publication_date":"2023-07-08","ids":{"openalex":"https://openalex.org/W4383618801","doi":"https://doi.org/10.1007/s10957-023-02261-w"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-023-02261-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-023-02261-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-023-02261-w.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","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/s10957-023-02261-w.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000135645","display_name":"Melinda Hagedorn","orcid":"https://orcid.org/0000-0003-2247-7216"},"institutions":[{"id":"https://openalex.org/I44260953","display_name":"Heinrich Heine University D\u00fcsseldorf","ror":"https://ror.org/024z2rq82","country_code":"DE","type":"education","lineage":["https://openalex.org/I44260953"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Melinda Hagedorn","raw_affiliation_strings":["Heinrich Heine University, D\u00fcsseldorf, Germany"],"raw_orcid":"https://orcid.org/0000-0003-2247-7216","affiliations":[{"raw_affiliation_string":"Heinrich Heine University, D\u00fcsseldorf, Germany","institution_ids":["https://openalex.org/I44260953"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015422470","display_name":"Florian Jarre","orcid":"https://orcid.org/0000-0003-3458-123X"},"institutions":[{"id":"https://openalex.org/I44260953","display_name":"Heinrich Heine University D\u00fcsseldorf","ror":"https://ror.org/024z2rq82","country_code":"DE","type":"education","lineage":["https://openalex.org/I44260953"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Florian Jarre","raw_affiliation_strings":["Heinrich Heine University, D\u00fcsseldorf, Germany"],"raw_orcid":"https://orcid.org/0000-0003-3458-123X","affiliations":[{"raw_affiliation_string":"Heinrich Heine University, D\u00fcsseldorf, Germany","institution_ids":["https://openalex.org/I44260953"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5000135645"],"corresponding_institution_ids":["https://openalex.org/I44260953"],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":{"value":3190,"currency":"USD","value_usd":3190},"fwci":0.3276,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.46842253,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"202","issue":"1","first_page":"456","last_page":"474"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9986000061035156,"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":0.9986000061035156,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.9972000122070312,"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/mathematics","display_name":"Mathematics","score":0.8256481885910034},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.6237151026725769},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5486571788787842},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5022366046905518},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4928464889526367},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48005470633506775},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.47802528738975525},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.46550968289375305},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.44581204652786255},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4299442172050476},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.37254512310028076},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23601442575454712},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11350357532501221}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8256481885910034},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.6237151026725769},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5486571788787842},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5022366046905518},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4928464889526367},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48005470633506775},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.47802528738975525},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.46550968289375305},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.44581204652786255},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4299442172050476},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.37254512310028076},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23601442575454712},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11350357532501221},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-023-02261-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-023-02261-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-023-02261-w.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:joptap:v:202:y:2024:i:1:d:10.1007_s10957-023-02261-w","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-023-02261-w","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":"article"}],"best_oa_location":{"id":"doi:10.1007/s10957-023-02261-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-023-02261-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-023-02261-w.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321951","display_name":"Heinrich-Heine-Universit\u00e4t D\u00fcsseldorf","ror":"https://ror.org/024z2rq82"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4383618801.pdf","grobid_xml":"https://content.openalex.org/works/W4383618801.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1573250193","https://openalex.org/W1988720110","https://openalex.org/W2017279613","https://openalex.org/W2127447444","https://openalex.org/W2604744755","https://openalex.org/W3136523593","https://openalex.org/W3141595720","https://openalex.org/W4221156640","https://openalex.org/W6638380949"],"related_works":["https://openalex.org/W2611031068","https://openalex.org/W1704347466","https://openalex.org/W4283017538","https://openalex.org/W1545275724","https://openalex.org/W2802707792","https://openalex.org/W1996936972","https://openalex.org/W2569979269","https://openalex.org/W2075777916","https://openalex.org/W3021699548","https://openalex.org/W2015677538"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"note":[2],"considers":[3],"the":[4,10,44,48,57,61,64,78,88,92,105,121,130],"momentum":[5,122,131],"method":[6,13,132],"by":[7,14,95],"Polyak":[8],"and":[9,37,40,124,133],"accelerated":[11,135],"gradient":[12,136],"Nesterov,":[15],"both":[16,103],"without":[17],"line":[18],"search":[19],"but":[20],"with":[21],"fixed":[22],"step":[23],"length":[24],"applied":[25],"to":[26,63,83,91,110],"strongly":[27],"convex":[28],"quadratic":[29],"functions":[30],"assuming":[31],"that":[32,56],"exact":[33],"gradients":[34],"are":[35,51],"used":[36],"appropriate":[38],"upper":[39],"lower":[41],"bounds":[42],"for":[43,120],"extreme":[45],"eigenvalues":[46],"of":[47,60,80,87,129],"Hessian":[49],"matrix":[50],"known.":[52],"Simple":[53],"2-d-examples":[54],"show":[55],"Euclidean":[58,89],"distance":[59,90],"iterates":[62],"optimal":[65,93,108,118],"solution":[66,94],"is":[67,75,107],"non-monotone.":[68],"In":[69],"this":[70],"context,":[71],"an":[72],"explicit":[73],"bound":[74,106],"derived":[76],"on":[77],"number":[79],"iterations":[81],"needed":[82],"guarantee":[84],"a":[85,96,111],"reduction":[86],"factor":[97],"$$\\epsilon":[98],"$$":[99],"\u03f5":[100],".":[101],"For":[102],"methods,":[104],"up":[109],"constant":[112],"factor,":[113],"it":[114,125],"complements":[115],"earlier":[116],"asymptotically":[117],"results":[119],"method,":[123],"establishes":[126],"another":[127],"link":[128],"Nesterov\u2019s":[134],"method.":[137]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}