{"id":"https://openalex.org/W4317396758","doi":"https://doi.org/10.1007/s11590-023-01972-3","title":"Almost sure convergence of stochastic composite objective mirror descent for non-convex non-smooth optimization","display_name":"Almost sure convergence of stochastic composite objective mirror descent for non-convex non-smooth optimization","publication_year":2023,"publication_date":"2023-01-18","ids":{"openalex":"https://openalex.org/W4317396758","doi":"https://doi.org/10.1007/s11590-023-01972-3"},"language":"en","primary_location":{"id":"doi:10.1007/s11590-023-01972-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-023-01972-3","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"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":"Optimization Letters","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/A5100934072","display_name":"Yuqing Liang","orcid":"https://orcid.org/0009-0008-5418-0760"},"institutions":[{"id":"https://openalex.org/I184983240","display_name":"Northeast Normal University","ror":"https://ror.org/02rkvz144","country_code":"CN","type":"education","lineage":["https://openalex.org/I184983240"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuqing Liang","raw_affiliation_strings":["Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, People\u2019s Republic of China","Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, People\u2019s Republic of China","institution_ids":["https://openalex.org/I184983240"]},{"raw_affiliation_string":"Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, People's Republic of China","institution_ids":["https://openalex.org/I184983240"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012826227","display_name":"Dongpo Xu","orcid":"https://orcid.org/0000-0002-9663-9743"},"institutions":[{"id":"https://openalex.org/I184983240","display_name":"Northeast Normal University","ror":"https://ror.org/02rkvz144","country_code":"CN","type":"education","lineage":["https://openalex.org/I184983240"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Dongpo Xu","raw_affiliation_strings":["Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, People\u2019s Republic of China","Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, People\u2019s Republic of China","institution_ids":["https://openalex.org/I184983240"]},{"raw_affiliation_string":"Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, People's Republic of China","institution_ids":["https://openalex.org/I184983240"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007758121","display_name":"Naimin Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I146620803","display_name":"Wenzhou University","ror":"https://ror.org/020hxh324","country_code":"CN","type":"education","lineage":["https://openalex.org/I146620803"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Naimin Zhang","raw_affiliation_strings":["College of Mathematics and Physics, Wenzhou University, Wenzhou, 325035, People\u2019s Republic of China","College of Mathematics and Physics, Wenzhou University, Wenzhou, 325035, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Physics, Wenzhou University, Wenzhou, 325035, People\u2019s Republic of China","institution_ids":["https://openalex.org/I146620803"]},{"raw_affiliation_string":"College of Mathematics and Physics, Wenzhou University, Wenzhou, 325035, People's Republic of China","institution_ids":["https://openalex.org/I146620803"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103001848","display_name":"Danilo P. Mandic","orcid":"https://orcid.org/0000-0001-8432-3963"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Danilo P. Mandic","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Imperial College London, London, SW7 2AZ, UK"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College London, London, SW7 2AZ, UK","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5012826227"],"corresponding_institution_ids":["https://openalex.org/I184983240"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.1766,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.51916441,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"18","issue":"9","first_page":"2113","last_page":"2131"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.9995999932289124,"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/T12676","display_name":"Machine Learning and ELM","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.8057868480682373},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.7033535242080688},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6927773952484131},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5791305303573608},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5380091071128845},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5261480212211609},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5051882863044739},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4724990129470825},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.47098255157470703},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4623355567455292},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4414406716823578},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.43369171023368835},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.41986095905303955},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23012623190879822},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.1810702383518219},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07725989818572998},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07378751039505005}],"concepts":[{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.8057868480682373},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.7033535242080688},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6927773952484131},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5791305303573608},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5380091071128845},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5261480212211609},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5051882863044739},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4724990129470825},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.47098255157470703},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4623355567455292},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4414406716823578},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.43369171023368835},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.41986095905303955},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23012623190879822},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.1810702383518219},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07725989818572998},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07378751039505005},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11590-023-01972-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-023-01972-3","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"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":"Optimization Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G286210498","display_name":null,"funder_award_id":"2021YFA1003400","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G5362080028","display_name":null,"funder_award_id":"2412020FZ024","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G7302374699","display_name":null,"funder_award_id":"62176051","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1994616650","https://openalex.org/W2029463628","https://openalex.org/W2038563976","https://openalex.org/W2142506503","https://openalex.org/W2157011125","https://openalex.org/W2489292218","https://openalex.org/W2497446532","https://openalex.org/W2807729763","https://openalex.org/W2896146108","https://openalex.org/W2901838001","https://openalex.org/W2963190258","https://openalex.org/W2963433607","https://openalex.org/W2963534244","https://openalex.org/W3020910274","https://openalex.org/W3034315405","https://openalex.org/W3035012470","https://openalex.org/W3119028331","https://openalex.org/W3211105213","https://openalex.org/W3212510276","https://openalex.org/W4214703365","https://openalex.org/W4236362309","https://openalex.org/W6600062020","https://openalex.org/W6607999579"],"related_works":["https://openalex.org/W2895097035","https://openalex.org/W4206903459","https://openalex.org/W2754816816","https://openalex.org/W4366280654","https://openalex.org/W3160167280","https://openalex.org/W4362706668","https://openalex.org/W4231621013","https://openalex.org/W3171021120","https://openalex.org/W3008318776","https://openalex.org/W4286899070"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-01-20T17:24:06.736184","created_date":"2025-10-10T00:00:00"}
