{"id":"https://openalex.org/W2795219137","doi":"https://doi.org/10.1007/s10957-018-1276-7","title":"On the Strong Convergence of Subgradients of Convex Functions","display_name":"On the Strong Convergence of Subgradients of Convex Functions","publication_year":2018,"publication_date":"2018-03-30","ids":{"openalex":"https://openalex.org/W2795219137","doi":"https://doi.org/10.1007/s10957-018-1276-7","mag":"2795219137"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-018-1276-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-018-1276-7","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":"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://doi.org/10.1007/s10957-018-1276-7","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061497144","display_name":"Dariusz Zagrodny","orcid":"https://orcid.org/0000-0001-9364-104X"},"institutions":[{"id":"https://openalex.org/I69984877","display_name":"Cardinal Stefan Wyszy\u0144ski University in Warsaw","ror":"https://ror.org/05sdyjv16","country_code":"PL","type":"education","lineage":["https://openalex.org/I69984877"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Dariusz Zagrodny","raw_affiliation_strings":["Faculty of Mathematics and Natural Sciences, College of Science, Cardinal Stefan Wyszy\u0144ski University, Dewajtis 5, Warsaw, Poland","Faculty of Mathematics and Natural Sciences, College of Science, Cardinal Stefan Wyszy\u0144ski University, Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Natural Sciences, College of Science, Cardinal Stefan Wyszy\u0144ski University, Dewajtis 5, Warsaw, Poland","institution_ids":["https://openalex.org/I69984877"]},{"raw_affiliation_string":"Faculty of Mathematics and Natural Sciences, College of Science, Cardinal Stefan Wyszy\u0144ski University, Warsaw, Poland","institution_ids":["https://openalex.org/I69984877"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5061497144"],"corresponding_institution_ids":["https://openalex.org/I69984877"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.2137,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.5319621,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"178","issue":"2","first_page":"411","last_page":"423"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9993000030517578,"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/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11545","display_name":"Advanced Banach Space Theory","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.8257237672805786},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.671988308429718},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.6594696044921875},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5835748910903931},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.583528995513916},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5727267265319824},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5688034296035767},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.5236737132072449},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5193975567817688},{"id":"https://openalex.org/keywords/proper-convex-function","display_name":"Proper convex function","score":0.4382632076740265},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4189777970314026},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36034727096557617},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3385451138019562},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3241042196750641},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11519593000411987},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.058517247438430786}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8257237672805786},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.671988308429718},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.6594696044921875},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5835748910903931},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.583528995513916},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5727267265319824},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5688034296035767},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.5236737132072449},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5193975567817688},{"id":"https://openalex.org/C50862404","wikidata":"https://www.wikidata.org/wiki/Q3075259","display_name":"Proper convex function","level":5,"score":0.4382632076740265},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4189777970314026},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36034727096557617},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3385451138019562},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3241042196750641},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11519593000411987},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.058517247438430786},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-018-1276-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-018-1276-7","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":"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:178:y:2018:i:2:d:10.1007_s10957-018-1276-7","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-018-1276-7","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/s10957-018-1276-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-018-1276-7","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":"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":[{"id":"https://metadata.un.org/sdg/10","score":0.6700000166893005,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W617646370","https://openalex.org/W1517403807","https://openalex.org/W1554916268","https://openalex.org/W1968916843","https://openalex.org/W2025077533","https://openalex.org/W2033427242","https://openalex.org/W2051984732","https://openalex.org/W2067896452","https://openalex.org/W2082380519","https://openalex.org/W2094599579","https://openalex.org/W2106731289","https://openalex.org/W2140263556","https://openalex.org/W2154265119","https://openalex.org/W2162162143","https://openalex.org/W2498059247","https://openalex.org/W3038830718","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2007576447","https://openalex.org/W2026600343","https://openalex.org/W2356261519","https://openalex.org/W4382519084","https://openalex.org/W2478309485","https://openalex.org/W165488893","https://openalex.org/W2040676043","https://openalex.org/W1510770274","https://openalex.org/W4361807553","https://openalex.org/W2185500298"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"results":[3],"on":[4],"the":[5,21,27,30],"strong":[6],"convergence":[7],"of":[8,10,29,32,34],"subgradients":[9],"convex":[11,36],"functions":[12],"along":[13,38],"a":[14,35,39],"given":[15,40],"direction":[16,41],"are":[17],"presented;":[18],"that":[19],"is,":[20],"relative":[22],"compactness":[23],"(with":[24],"respect":[25],"to":[26],"norm)":[28],"union":[31],"subdifferentials":[33],"function":[37],"is":[42],"investigated.":[43]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
