{"id":"https://openalex.org/W2926523766","doi":"https://doi.org/10.1007/s10957-019-01516-9","title":"On Linear Convergence of Non-Euclidean Gradient Methods without Strong Convexity and Lipschitz Gradient Continuity","display_name":"On Linear Convergence of Non-Euclidean Gradient Methods without Strong Convexity and Lipschitz Gradient Continuity","publication_year":2019,"publication_date":"2019-04-05","ids":{"openalex":"https://openalex.org/W2926523766","doi":"https://doi.org/10.1007/s10957-019-01516-9","mag":"2926523766"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-019-01516-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-019-01516-9","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/A5106498524","display_name":"Heinz H. Bauschke","orcid":"https://orcid.org/0000-0002-4155-9930"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]},{"id":"https://openalex.org/I4405260628","display_name":"University of British Columbia, Okanagan Campus","ror":"https://ror.org/04241wz75","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490","https://openalex.org/I4405260628"]},{"id":"https://openalex.org/I822440","display_name":"Okanagan University College","ror":"https://ror.org/02mxmh518","country_code":"CA","type":"education","lineage":["https://openalex.org/I822440"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Heinz H. Bauschke","raw_affiliation_strings":["Department of Mathematics, Irving K. Barber School, University of British Columbia Okanagan, Kelowna, BC, V1V 1V7, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Irving K. Barber School, University of British Columbia Okanagan, Kelowna, BC, V1V 1V7, Canada","institution_ids":["https://openalex.org/I822440","https://openalex.org/I141945490","https://openalex.org/I4405260628"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049386571","display_name":"J\u00e9r\u00f4me Bolte","orcid":"https://orcid.org/0000-0002-1676-8407"},"institutions":[{"id":"https://openalex.org/I4210092408","display_name":"Toulouse School of Economics","ror":"https://ror.org/00ff5f522","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210092408"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"J\u00e9r\u00f4me Bolte","raw_affiliation_strings":["Toulouse School of Economics, Universit\u00e9 Toulouse 1 Capitole, 31015, Toulouse, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Toulouse School of Economics, Universit\u00e9 Toulouse 1 Capitole, 31015, Toulouse, France","institution_ids":["https://openalex.org/I4210092408"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100362816","display_name":"Jiawei Chen","orcid":"https://orcid.org/0000-0002-4874-3415"},"institutions":[{"id":"https://openalex.org/I142108993","display_name":"Southwest University","ror":"https://ror.org/01kj4z117","country_code":"CN","type":"education","lineage":["https://openalex.org/I142108993"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiawei Chen","raw_affiliation_strings":["School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China","institution_ids":["https://openalex.org/I142108993"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041397571","display_name":"Marc Teboulle","orcid":"https://orcid.org/0000-0002-4228-131X"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Marc Teboulle","raw_affiliation_strings":["School of Mathematical Sciences, Tel Aviv University, 69978, Ramat Aviv, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Tel Aviv University, 69978, Ramat Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005122439","display_name":"Xianfu Wang","orcid":"https://orcid.org/0000-0002-2066-7473"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]},{"id":"https://openalex.org/I4405260628","display_name":"University of British Columbia, Okanagan Campus","ror":"https://ror.org/04241wz75","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490","https://openalex.org/I4405260628"]},{"id":"https://openalex.org/I822440","display_name":"Okanagan University College","ror":"https://ror.org/02mxmh518","country_code":"CA","type":"education","lineage":["https://openalex.org/I822440"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Xianfu Wang","raw_affiliation_strings":["Department of Mathematics, Irving K. Barber School, University of British Columbia Okanagan, Kelowna, BC, V1V 1V7, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Irving K. Barber School, University of British Columbia Okanagan, Kelowna, BC, V1V 1V7, Canada","institution_ids":["https://openalex.org/I822440","https://openalex.org/I141945490","https://openalex.org/I4405260628"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5049386571"],"corresponding_institution_ids":["https://openalex.org/I4210092408"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":3.6388,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.93540865,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"182","issue":"3","first_page":"1068","last_page":"1087"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9984999895095825,"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":0.9984999895095825,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.998199999332428,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9979000091552734,"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/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.8809114098548889},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.823563814163208},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.819251537322998},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6256272792816162},{"id":"https://openalex.org/keywords/proximal-gradient-methods","display_name":"Proximal Gradient Methods","score":0.5484212636947632},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5429356694221497},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5336201190948486},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4887104034423828},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.46890485286712646},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.45020100474357605},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.4404177963733673},{"id":"https://openalex.org/keywords/bregman-divergence","display_name":"Bregman divergence","score":0.43401965498924255},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.4320743978023529},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4232545495033264},{"id":"https://openalex.org/keywords/balanced-flow","display_name":"Balanced flow","score":0.4226521849632263},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42215192317962646},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.38363635540008545},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.31847065687179565},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12739816308021545},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09327039122581482},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08495849370956421}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8809114098548889},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.823563814163208},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.819251537322998},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6256272792816162},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.5484212636947632},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5429356694221497},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5336201190948486},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4887104034423828},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.46890485286712646},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45020100474357605},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.4404177963733673},{"id":"https://openalex.org/C149073432","wikidata":"https://www.wikidata.org/wiki/Q4960382","display_name":"Bregman divergence","level":2,"score":0.43401965498924255},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.4320743978023529},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4232545495033264},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.4226521849632263},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42215192317962646},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.38363635540008545},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.31847065687179565},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12739816308021545},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09327039122581482},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08495849370956421},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"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/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-019-01516-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-019-01516-9","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:182:y:2019:i:3:d:10.1007_s10957-019-01516-9","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-019-01516-9","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":[{"id":"https://openalex.org/G8495029215","display_name":"Optimisation on Measures Spaces","funder_award_id":"ANR-17-CE23-0013","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W205960364","https://openalex.org/W562372631","https://openalex.org/W1505731132","https://openalex.org/W1551360398","https://openalex.org/W1569098853","https://openalex.org/W1604467579","https://openalex.org/W1979207064","https://openalex.org/W1986891697","https://openalex.org/W2004304255","https://openalex.org/W2009274429","https://openalex.org/W2016384870","https://openalex.org/W2021361347","https://openalex.org/W2032330602","https://openalex.org/W2033468335","https://openalex.org/W2033511209","https://openalex.org/W2062106836","https://openalex.org/W2079576032","https://openalex.org/W2082334903","https://openalex.org/W2090376964","https://openalex.org/W2100556411","https://openalex.org/W2112980792","https://openalex.org/W2139759436","https://openalex.org/W2161209207","https://openalex.org/W2163803752","https://openalex.org/W2551153860","https://openalex.org/W2763081248","https://openalex.org/W2798766386","https://openalex.org/W2800693632","https://openalex.org/W2962706047","https://openalex.org/W2962826994","https://openalex.org/W2963967579","https://openalex.org/W2990138404","https://openalex.org/W3037678684","https://openalex.org/W3141595720","https://openalex.org/W4242766606","https://openalex.org/W4249667877","https://openalex.org/W6600281463","https://openalex.org/W6634116496"],"related_works":["https://openalex.org/W2905950575","https://openalex.org/W2963086517","https://openalex.org/W2564735875","https://openalex.org/W3123504125","https://openalex.org/W3147739796","https://openalex.org/W1983212821","https://openalex.org/W3127841625","https://openalex.org/W2594900731","https://openalex.org/W2811217697","https://openalex.org/W2364728921"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-20T22:02:38.213706","created_date":"2025-10-10T00:00:00"}