{"id":"https://openalex.org/W3025217413","doi":"https://doi.org/10.1007/s10957-020-01677-y","title":"Analysis of the Barzilai-Borwein Step-Sizes for Problems in Hilbert Spaces","display_name":"Analysis of the Barzilai-Borwein Step-Sizes for Problems in Hilbert Spaces","publication_year":2020,"publication_date":"2020-05-13","ids":{"openalex":"https://openalex.org/W3025217413","doi":"https://doi.org/10.1007/s10957-020-01677-y","mag":"3025217413"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-020-01677-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-020-01677-y","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":"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/A5021642306","display_name":"Behzad Azmi","orcid":"https://orcid.org/0000-0002-6303-254X"},"institutions":[{"id":"https://openalex.org/I4210158379","display_name":"Johann Radon Institute for Computational and Applied Mathematics","ror":"https://ror.org/05a94k872","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I4210158379"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Behzad Azmi","raw_affiliation_strings":["Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Science, Altenberger Stra\u00dfe 69, 4040, Linz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Science, Altenberger Stra\u00dfe 69, 4040, Linz, Austria","institution_ids":["https://openalex.org/I4210158379"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074607617","display_name":"Karl Kunisch","orcid":"https://orcid.org/0000-0003-1113-7355"},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]},{"id":"https://openalex.org/I4210158379","display_name":"Johann Radon Institute for Computational and Applied Mathematics","ror":"https://ror.org/05a94k872","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I4210158379"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Karl Kunisch","raw_affiliation_strings":["Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstra\u00dfe 36, 8010, Graz, Austria","Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Science, Altenberger Stra\u00dfe 69, 4040, Linz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstra\u00dfe 36, 8010, Graz, Austria","institution_ids":["https://openalex.org/I15766117"]},{"raw_affiliation_string":"Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Science, Altenberger Stra\u00dfe 69, 4040, Linz, Austria","institution_ids":["https://openalex.org/I4210158379"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":3.5659,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.93070902,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"185","issue":"3","first_page":"819","last_page":"844"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9991000294685364,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9984999895095825,"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":0.8626763820648193},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.7116620540618896},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6070343255996704},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5554778575897217},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46714991331100464},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.42592141032218933},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3587559759616852},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.347040593624115},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1834610104560852}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8626763820648193},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.7116620540618896},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6070343255996704},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5554778575897217},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46714991331100464},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.42592141032218933},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3587559759616852},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.347040593624115},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1834610104560852},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-020-01677-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-020-01677-y","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:RePEc:spr:joptap:v:185:y:2020:i:3:d:10.1007_s10957-020-01677-y","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-020-01677-y","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":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W141901529","https://openalex.org/W173320072","https://openalex.org/W647986212","https://openalex.org/W1480857162","https://openalex.org/W1497361805","https://openalex.org/W1597209545","https://openalex.org/W1963847819","https://openalex.org/W1980053021","https://openalex.org/W1982067912","https://openalex.org/W1983163996","https://openalex.org/W2023311343","https://openalex.org/W2034926269","https://openalex.org/W2048023783","https://openalex.org/W2050096287","https://openalex.org/W2070580109","https://openalex.org/W2076605490","https://openalex.org/W2090287784","https://openalex.org/W2093575660","https://openalex.org/W2109062572","https://openalex.org/W2140163944","https://openalex.org/W2141163505","https://openalex.org/W2182853125","https://openalex.org/W2331960290","https://openalex.org/W2483549946","https://openalex.org/W2522336029","https://openalex.org/W2739680746","https://openalex.org/W4302819252"],"related_works":["https://openalex.org/W4250775169","https://openalex.org/W1517908938","https://openalex.org/W4309231192","https://openalex.org/W2064563243","https://openalex.org/W3165104833","https://openalex.org/W2012783289","https://openalex.org/W2281834912","https://openalex.org/W1489941249","https://openalex.org/W2018678701","https://openalex.org/W1983109191"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}