{"id":"https://openalex.org/W3002730424","doi":"https://doi.org/10.1007/s10957-020-01632-x","title":"On the Quality of First-Order Approximation of Functions with H\u00f6lder Continuous Gradient","display_name":"On the Quality of First-Order Approximation of Functions with H\u00f6lder Continuous Gradient","publication_year":2020,"publication_date":"2020-02-11","ids":{"openalex":"https://openalex.org/W3002730424","doi":"https://doi.org/10.1007/s10957-020-01632-x","mag":"3002730424"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-020-01632-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-020-01632-x","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2001.07946","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087306498","display_name":"Guillaume O. Berger","orcid":"https://orcid.org/0000-0002-0633-8948"},"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":"Guillaume O. Berger","raw_affiliation_strings":["UCLouvain, Louvain-la-Neuve, Belgium"],"affiliations":[{"raw_affiliation_string":"UCLouvain, Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034347171","display_name":"P.-A. Absil","orcid":"https://orcid.org/0000-0003-2946-4178"},"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":false,"raw_author_name":"P.-A. Absil","raw_affiliation_strings":["UCLouvain, Louvain-la-Neuve, Belgium"],"affiliations":[{"raw_affiliation_string":"UCLouvain, Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056625594","display_name":"Rapha\u00ebl M. Jungers","orcid":"https://orcid.org/0000-0002-7789-0940"},"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":false,"raw_author_name":"Rapha\u00ebl M. Jungers","raw_affiliation_strings":["UCLouvain, Louvain-la-Neuve, Belgium"],"affiliations":[{"raw_affiliation_string":"UCLouvain, Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]},{"author_position":"last","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":false,"raw_author_name":"Yurii Nesterov","raw_affiliation_strings":["UCLouvain, Louvain-la-Neuve, Belgium"],"affiliations":[{"raw_affiliation_string":"UCLouvain, Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5087306498"],"corresponding_institution_ids":["https://openalex.org/I95674353"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.2958,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.46554935,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"185","issue":"1","first_page":"17","last_page":"33"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983999729156494,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983999729156494,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9980000257492065,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9980000257492065,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.8878498673439026},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.7306092381477356},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6882942914962769},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.6764358282089233},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6547600030899048},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6112575531005859},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5889366865158081},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5077970623970032},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4913586676120758},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.4144229292869568},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4127941131591797},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.19782480597496033},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12933728098869324},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07097229361534119}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8878498673439026},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.7306092381477356},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6882942914962769},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.6764358282089233},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6547600030899048},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6112575531005859},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5889366865158081},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5077970623970032},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4913586676120758},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.4144229292869568},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4127941131591797},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.19782480597496033},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12933728098869324},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07097229361534119},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1007/s10957-020-01632-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-020-01632-x","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2001.07946","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.07946","pdf_url":"https://arxiv.org/pdf/2001.07946","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":"mag:3002730424","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2001.07946","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:RePEc:cor:louvrp:3102","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:RePEc:spr:joptap:v:185:y:2020:i:1:d:10.1007_s10957-020-01632-x","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-020-01632-x","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"},{"id":"pmh:oai:dial.uclouvain.be:boreal:227384","is_oa":true,"landing_page_url":"http://hdl.handle.net/2078.1/227384","pdf_url":null,"source":{"id":"https://openalex.org/S4306400166","display_name":"Digital Access to Libraries","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2800384882","host_organization_name":"Harris County Public Library","host_organization_lineage":["https://openalex.org/I2800384882"],"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":"Journal of Optimization Theory and Applications, Vol. 185, p. 17-33 (2020)","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.2001.07946","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2001.07946","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2001.07946","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.07946","pdf_url":"https://arxiv.org/pdf/2001.07946","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"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.44999998807907104,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W113482007","https://openalex.org/W187211397","https://openalex.org/W1518096223","https://openalex.org/W1565485340","https://openalex.org/W1568307856","https://openalex.org/W1965099828","https://openalex.org/W1985240368","https://openalex.org/W2027470314","https://openalex.org/W2030161963","https://openalex.org/W2155823647","https://openalex.org/W2272094913","https://openalex.org/W2402588523","https://openalex.org/W3141595720","https://openalex.org/W6638380949"],"related_works":["https://openalex.org/W1977412820","https://openalex.org/W3147777701","https://openalex.org/W2095413357","https://openalex.org/W2183107660","https://openalex.org/W2089444355","https://openalex.org/W3133514242","https://openalex.org/W270792462","https://openalex.org/W1977748449","https://openalex.org/W2501746113","https://openalex.org/W22671108","https://openalex.org/W1997596807","https://openalex.org/W2799213582","https://openalex.org/W3100555527","https://openalex.org/W2272204794","https://openalex.org/W2889795689","https://openalex.org/W2242222483","https://openalex.org/W40682927","https://openalex.org/W3025065608","https://openalex.org/W101074022","https://openalex.org/W2135959906"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}