{"id":"https://openalex.org/W2985545095","doi":"https://doi.org/10.1007/s11590-021-01753-w","title":"On the rate of convergence of alternating minimization for non-smooth non-strongly convex optimization in Banach spaces","display_name":"On the rate of convergence of alternating minimization for non-smooth non-strongly convex optimization in Banach spaces","publication_year":2021,"publication_date":"2021-05-24","ids":{"openalex":"https://openalex.org/W2985545095","doi":"https://doi.org/10.1007/s11590-021-01753-w","mag":"2985545095"},"language":"en","primary_location":{"id":"doi:10.1007/s11590-021-01753-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11590-021-01753-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11590-021-01753-w.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11590-021-01753-w.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Jakub Wiktor Both","orcid":"https://orcid.org/0000-0001-6131-4976"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":true,"raw_author_name":"Jakub Wiktor Both","raw_affiliation_strings":["Department of Mathematics, University of Bergen, Bergen, Norway"],"raw_orcid":"https://orcid.org/0000-0001-6131-4976","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Bergen, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4432739"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.4542,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.65289285,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"16","issue":"2","first_page":"729","last_page":"743"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9812999963760376,"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":0.9812999963760376,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.004900000058114529,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.0026000000070780516,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/sublinear-function","display_name":"Sublinear function","score":0.8223000168800354},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.6471999883651733},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.630299985408783},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6168000102043152},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5551999807357788},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5105000138282776},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5042999982833862},{"id":"https://openalex.org/keywords/modes-of-convergence","display_name":"Modes of convergence (annotated index)","score":0.4997999966144562},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.44589999318122864}],"concepts":[{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.8223000168800354},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7936000227928162},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.6471999883651733},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.630299985408783},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6168000102043152},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5551999807357788},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5105000138282776},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5042999982833862},{"id":"https://openalex.org/C48216909","wikidata":"https://www.wikidata.org/wiki/Q6889156","display_name":"Modes of convergence (annotated index)","level":5,"score":0.4997999966144562},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45989999175071716},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.44589999318122864},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3828999996185303},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.3709000051021576},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3652999997138977},{"id":"https://openalex.org/C5871375","wikidata":"https://www.wikidata.org/wiki/Q1780715","display_name":"Compact convergence","level":4,"score":0.3614000082015991},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.350600004196167},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.34869998693466187},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.34450000524520874},{"id":"https://openalex.org/C14928880","wikidata":"https://www.wikidata.org/wiki/Q1512559","display_name":"Normal convergence","level":4,"score":0.3411000072956085},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.32100000977516174},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3199000060558319},{"id":"https://openalex.org/C38487692","wikidata":"https://www.wikidata.org/wiki/Q1067156","display_name":"Dominated convergence theorem","level":5,"score":0.2824999988079071},{"id":"https://openalex.org/C538505008","wikidata":"https://www.wikidata.org/wiki/Q3979448","display_name":"Convergence tests","level":4,"score":0.27559998631477356},{"id":"https://openalex.org/C123413131","wikidata":"https://www.wikidata.org/wiki/Q847535","display_name":"Uniformly convex space","level":5,"score":0.2736000120639801},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2662000060081482},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.2567000091075897}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11590-021-01753-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11590-021-01753-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11590-021-01753-w.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1911.00404","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1911.00404","pdf_url":"https://arxiv.org/pdf/1911.00404","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"}],"best_oa_location":{"id":"doi:10.1007/s11590-021-01753-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11590-021-01753-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11590-021-01753-w.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323078","display_name":"Universitetet i Bergen","ror":"https://ror.org/03zga2b32"},{"id":"https://openalex.org/F4320326507","display_name":"Haukeland\u00a0Universitetssjukehus","ror":"https://ror.org/03np4e098"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2985545095.pdf","grobid_xml":"https://content.openalex.org/works/W2985545095.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1982518801","https://openalex.org/W2000769684","https://openalex.org/W2023901033","https://openalex.org/W2027361795","https://openalex.org/W2035507034","https://openalex.org/W2082639035","https://openalex.org/W2087714402","https://openalex.org/W2093417350","https://openalex.org/W2151718183","https://openalex.org/W2963830980","https://openalex.org/W3112401890","https://openalex.org/W6602139238"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper,":[3],"the":[4,7,51,83],"convergence":[5,26,86,95],"of":[6,25,34,48,56,82],"fundamental":[8],"alternating":[9],"minimization":[10],"is":[11,42,87,96],"established":[12],"for":[13,89,98],"non-smooth":[14,40],"non-strongly":[15],"convex":[16],"optimization":[17],"problems":[18],"in":[19],"Banach":[20],"spaces,":[21],"and":[22,37,68,74,91],"novel":[23],"rates":[24,76],"are":[27,59],"provided.":[28],"As":[29],"objective":[30],"function":[31],"a":[32,35,38,45],"composition":[33],"smooth,":[36],"block-separable,":[39],"part":[41],"considered,":[43],"covering":[44],"large":[46],"range":[47],"applications.":[49],"For":[50],"former,":[52],"three":[53],"different":[54],"relaxations":[55],"strong":[57],"convexity":[58],"considered:":[60],"(i)":[61,90],"quasi-strong":[62],"convexity;":[63],"(ii)":[64],"quadratic":[65],"functional":[66],"growth;":[67],"(iii)":[69],"plain":[70],"convexity.":[71],"With":[72],"new":[73],"improved":[75],"benefiting":[77],"from":[78],"both":[79],"separate":[80],"steps":[81],"scheme,":[84],"linear":[85],"proved":[88],"(ii),":[92],"whereas":[93],"sublinear":[94],"showed":[97],"(iii).":[99]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2019-11-22T00:00:00"}