{"id":"https://openalex.org/W4229050742","doi":"https://doi.org/10.1007/s10957-022-02013-2","title":"Quadratic Growth Conditions and Uniqueness of Optimal Solution to Lasso","display_name":"Quadratic Growth Conditions and Uniqueness of Optimal Solution to Lasso","publication_year":2022,"publication_date":"2022-03-25","ids":{"openalex":"https://openalex.org/W4229050742","doi":"https://doi.org/10.1007/s10957-022-02013-2"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-022-02013-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-022-02013-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-022-02013-2.pdf","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://link.springer.com/content/pdf/10.1007/s10957-022-02013-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015159689","display_name":"Yunier Bello-Cruz","orcid":"https://orcid.org/0000-0002-7877-5688"},"institutions":[{"id":"https://openalex.org/I102502594","display_name":"Northern Illinois University","ror":"https://ror.org/012wxa772","country_code":"US","type":"education","lineage":["https://openalex.org/I102502594"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yunier Bello-Cruz","raw_affiliation_strings":["Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA","Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL, 60115, USA"],"raw_orcid":"https://orcid.org/0000-0002-7877-5688","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA","institution_ids":["https://openalex.org/I102502594"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL, 60115, USA","institution_ids":["https://openalex.org/I102502594"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025579166","display_name":"Guoyin Li","orcid":"https://orcid.org/0000-0002-2099-7974"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Guoyin Li","raw_affiliation_strings":["Department of Applied Mathematics, University of New South Wales, Sydney 2052, Australia","Department of Applied Mathematics, University of New South Wales, Sydney, 2052, Australia"],"raw_orcid":"https://orcid.org/0000-0002-2099-7974","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of New South Wales, Sydney 2052, Australia","institution_ids":["https://openalex.org/I31746571"]},{"raw_affiliation_string":"Department of Applied Mathematics, University of New South Wales, Sydney, 2052, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075913105","display_name":"T. T. A. Nghia","orcid":"https://orcid.org/0000-0001-7016-6450"},"institutions":[{"id":"https://openalex.org/I177721651","display_name":"Oakland University","ror":"https://ror.org/01ythxj32","country_code":"US","type":"education","lineage":["https://openalex.org/I177721651"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tran Thai An Nghia","raw_affiliation_strings":["Department of Mathematics and Statistics, Oakland University, Rochester, MI, 48309, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Oakland University, Rochester, MI, 48309, USA","institution_ids":["https://openalex.org/I177721651"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5025579166"],"corresponding_institution_ids":["https://openalex.org/I31746571"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.5085,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.84201723,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"194","issue":"1","first_page":"167","last_page":"190"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9972000122070312,"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":0.9972000122070312,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.8254177570343018},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7738295197486877},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6060335636138916},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5860447287559509},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5768048167228699},{"id":"https://openalex.org/keywords/lasso","display_name":"Lasso (programming language)","score":0.4761410057544708},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44550079107284546},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27866053581237793},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11068525910377502},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09145760536193848},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08230629563331604}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8254177570343018},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7738295197486877},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6060335636138916},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5860447287559509},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5768048167228699},{"id":"https://openalex.org/C37616216","wikidata":"https://www.wikidata.org/wiki/Q3218363","display_name":"Lasso (programming language)","level":2,"score":0.4761410057544708},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44550079107284546},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27866053581237793},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11068525910377502},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09145760536193848},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08230629563331604},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-022-02013-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-022-02013-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-022-02013-2.pdf","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:194:y:2022:i:1:d:10.1007_s10957-022-02013-2","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-022-02013-2","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/s10957-022-02013-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-022-02013-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-022-02013-2.pdf","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":[],"awards":[{"id":"https://openalex.org/G3711163969","display_name":null,"funder_award_id":"1816386","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7234939700","display_name":null,"funder_award_id":"DP190100555","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G967666175","display_name":null,"funder_award_id":"1816449","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4229050742.pdf","grobid_xml":"https://content.openalex.org/works/W4229050742.grobid-xml"},"referenced_works_count":50,"referenced_works":["https://openalex.org/W1495241813","https://openalex.org/W1848983290","https://openalex.org/W1946620893","https://openalex.org/W1967374611","https://openalex.org/W1986737463","https://openalex.org/W2006262045","https://openalex.org/W2009702064","https://openalex.org/W2039050532","https://openalex.org/W2044615981","https://openalex.org/W2055467852","https://openalex.org/W2060262297","https://openalex.org/W2093417350","https://openalex.org/W2115706991","https://openalex.org/W2127300249","https://openalex.org/W2130025383","https://openalex.org/W2135046866","https://openalex.org/W2147656689","https://openalex.org/W2152204644","https://openalex.org/W2155727363","https://openalex.org/W2155969596","https://openalex.org/W2156364114","https://openalex.org/W2157969180","https://openalex.org/W2167077875","https://openalex.org/W2216134724","https://openalex.org/W2257998465","https://openalex.org/W2265744594","https://openalex.org/W2271221198","https://openalex.org/W2513710035","https://openalex.org/W2551153860","https://openalex.org/W2587989539","https://openalex.org/W2962688058","https://openalex.org/W2962704982","https://openalex.org/W2962826994","https://openalex.org/W2963177878","https://openalex.org/W2963254198","https://openalex.org/W2963353224","https://openalex.org/W2963830980","https://openalex.org/W2963912922","https://openalex.org/W2963991544","https://openalex.org/W2964094444","https://openalex.org/W3098520355","https://openalex.org/W3100208521","https://openalex.org/W3101710822","https://openalex.org/W3106800919","https://openalex.org/W3182599367","https://openalex.org/W4229650096","https://openalex.org/W4231183558","https://openalex.org/W4244393449","https://openalex.org/W4249513058","https://openalex.org/W4252317729"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W4301247218","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W2129818458","https://openalex.org/W4289551052","https://openalex.org/W4390756076","https://openalex.org/W4243074410","https://openalex.org/W2969742028"],"abstract_inverted_index":{"Abstract":[0],"In":[1,40],"the":[2,17,30,45,72,80,101],"previous":[3],"paper":[4],"Bello-Cruz":[5],"et":[6],"al.":[7],"(J":[8],"Optim":[9],"Theory":[10],"Appl":[11],"188:378\u2013401,":[12],"2021),":[13],"we":[14,43,94],"showed":[15],"that":[16,60],"quadratic":[18,48],"growth":[19,49],"condition":[20,50],"plays":[21],"a":[22,89],"key":[23],"role":[24],"in":[25,62,116],"obtaining":[26],"Q-linear":[27],"convergence":[28],"of":[29,47,91,103],"widely":[31],"used":[32],"forward\u2013backward":[33],"splitting":[34],"method":[35],"with":[36],"Beck\u2013Teboulle\u2019s":[37],"line":[38],"search.":[39],"this":[41,92,117],"paper,":[42],"analyze":[44],"property":[46],"via":[51],"second-order":[52],"variational":[53],"analysis":[54],"for":[55,70,100],"various":[56],"structured":[57],"optimization":[58,86],"problems":[59],"arise":[61],"machine":[63],"learning":[64],"and":[65,111],"signal":[66],"processing.":[67],"This":[68],"includes,":[69],"example,":[71],"Poisson":[73],"linear":[74],"inverse":[75],"problem":[76],"as":[77,79],"well":[78],"$$\\ell":[81],"_1$$":[82],"<mml:math":[83],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mi>\u2113</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math>":[84],"-regularized":[85],"problems.":[87],"As":[88],"by-product":[90],"approach,":[93],"also":[95],"obtain":[96],"several":[97],"full":[98],"characterizations":[99],"uniqueness":[102],"optimal":[104],"solution":[105],"to":[106],"Lasso":[107],"problem,":[108],"which":[109],"complements":[110],"extends":[112],"recent":[113],"important":[114],"results":[115],"direction.":[118]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
