{"id":"https://openalex.org/W2004461831","doi":"https://doi.org/10.1007/s10589-006-6446-0","title":"Gradient Methods with Adaptive Step-Sizes","display_name":"Gradient Methods with Adaptive Step-Sizes","publication_year":2006,"publication_date":"2006-03-31","ids":{"openalex":"https://openalex.org/W2004461831","doi":"https://doi.org/10.1007/s10589-006-6446-0","mag":"2004461831"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-006-6446-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-006-6446-0","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"Computational Optimization and Applications","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/A5080074993","display_name":"Bin Zhou","orcid":"https://orcid.org/0000-0001-7595-4798"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bin Zhou","raw_affiliation_strings":["School of Mathematical Sciences and LMAM, Peking University, Beijing, 100871, People\u2019s Republic of China","School of Mathematical Sciences and LMAM, Peking University, Beijing, People's Republic of China 100871#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and LMAM, Peking University, Beijing, 100871, People\u2019s Republic of China","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"School of Mathematical Sciences and LMAM, Peking University, Beijing, People's Republic of China 100871#TAB#","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087399822","display_name":"Li Gao","orcid":"https://orcid.org/0000-0001-8858-129X"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Gao","raw_affiliation_strings":["School of Mathematical Sciences and LMAM, Peking University, Beijing, 100871, People\u2019s Republic of China","School of Mathematical Sciences and LMAM, Peking University, Beijing, People's Republic of China 100871#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and LMAM, Peking University, Beijing, 100871, People\u2019s Republic of China","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"School of Mathematical Sciences and LMAM, Peking University, Beijing, People's Republic of China 100871#TAB#","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109187979","display_name":"Yu\u2010Hong Dai","orcid":"https://orcid.org/0000-0002-6932-9512"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu-Hong Dai","raw_affiliation_strings":["State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P. O. Box 2719, Beijing, 100080, People\u2019s Republic of China","State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Acade ...#TAB#"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P. O. Box 2719, Beijing, 100080, People\u2019s Republic of China","institution_ids":["https://openalex.org/I4210120485"]},{"raw_affiliation_string":"State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Acade ...#TAB#","institution_ids":["https://openalex.org/I4210120485"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5080074993"],"corresponding_institution_ids":["https://openalex.org/I20231570"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":4.5257,"has_fulltext":false,"cited_by_count":207,"citation_normalized_percentile":{"value":0.94041386,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"35","issue":"1","first_page":"69","last_page":"86"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9997000098228455,"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":0.9997000098228455,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9986000061035156,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9921000003814697,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8495585918426514},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6297218799591064},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5669384598731995},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.5510957837104797},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5139672160148621},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.41621631383895874},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3919031023979187},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3712065517902374},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10993567109107971},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08933421969413757}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8495585918426514},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6297218799591064},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5669384598731995},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.5510957837104797},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5139672160148621},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.41621631383895874},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3919031023979187},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3712065517902374},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10993567109107971},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08933421969413757},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10589-006-6446-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-006-6446-0","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"Computational Optimization and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/13","score":0.5299999713897705,"display_name":"Climate action"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1214698286","https://openalex.org/W1493249195","https://openalex.org/W1497361805","https://openalex.org/W1530695493","https://openalex.org/W1966518481","https://openalex.org/W1973734200","https://openalex.org/W1976507361","https://openalex.org/W1978100686","https://openalex.org/W1982067912","https://openalex.org/W1983212821","https://openalex.org/W2000218110","https://openalex.org/W2012341322","https://openalex.org/W2012564502","https://openalex.org/W2031127394","https://openalex.org/W2039771911","https://openalex.org/W2041187281","https://openalex.org/W2043430160","https://openalex.org/W2045010238","https://openalex.org/W2050096287","https://openalex.org/W2076605490","https://openalex.org/W2122720079","https://openalex.org/W2166308223","https://openalex.org/W2167137033","https://openalex.org/W2316564661","https://openalex.org/W4205795514","https://openalex.org/W4242229293","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2846499288","https://openalex.org/W2075961230","https://openalex.org/W263682811","https://openalex.org/W2564172750","https://openalex.org/W3197592642","https://openalex.org/W3199158697","https://openalex.org/W2356977358","https://openalex.org/W2302465375","https://openalex.org/W2098528027","https://openalex.org/W2088605360"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":18},{"year":2023,"cited_by_count":15},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":19},{"year":2019,"cited_by_count":15},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":14},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":13},{"year":2012,"cited_by_count":11}],"updated_date":"2026-04-24T08:23:43.765630","created_date":"2025-10-10T00:00:00"}
