{"id":"https://openalex.org/W4405269795","doi":"https://doi.org/10.1109/lcsys.2024.3516632","title":"Proximal Gradient Dynamics: Monotonicity, Exponential Convergence, and Applications","display_name":"Proximal Gradient Dynamics: Monotonicity, Exponential Convergence, and Applications","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4405269795","doi":"https://doi.org/10.1109/lcsys.2024.3516632"},"language":"en","primary_location":{"id":"doi:10.1109/lcsys.2024.3516632","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcsys.2024.3516632","pdf_url":null,"source":{"id":"https://openalex.org/S4306422535","display_name":"IEEE Control Systems Letters","issn_l":"2475-1456","issn":["2475-1456"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Control Systems 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/A5080330764","display_name":"Anand Gokhale","orcid":"https://orcid.org/0000-0002-0569-2785"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]},{"id":"https://openalex.org/I4210140143","display_name":"Dynamic Systems (United States)","ror":"https://ror.org/043vm9914","country_code":"US","type":"company","lineage":["https://openalex.org/I4210140143"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Anand Gokhale","raw_affiliation_strings":["Center for Control, Dynamical Systems, and Computation, UC Santa Barbara, Santa Barbara, CA, USA","Dynamical Systems, and Computation, Center for Control, UC Santa Barbara, Santa Barbara, CA, USA"],"raw_orcid":"https://orcid.org/0000-0002-0569-2785","affiliations":[{"raw_affiliation_string":"Center for Control, Dynamical Systems, and Computation, UC Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I4210140143","https://openalex.org/I154570441"]},{"raw_affiliation_string":"Dynamical Systems, and Computation, Center for Control, UC Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I4210140143","https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059595265","display_name":"A. S. Davydov","orcid":"https://orcid.org/0000-0001-5629-2565"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]},{"id":"https://openalex.org/I4210140143","display_name":"Dynamic Systems (United States)","ror":"https://ror.org/043vm9914","country_code":"US","type":"company","lineage":["https://openalex.org/I4210140143"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alexander Davydov","raw_affiliation_strings":["Center for Control, Dynamical Systems, and Computation, UC Santa Barbara, Santa Barbara, CA, USA","Dynamical Systems, and Computation, Center for Control, UC Santa Barbara, Santa Barbara, CA, USA"],"raw_orcid":"https://orcid.org/0000-0001-5629-2565","affiliations":[{"raw_affiliation_string":"Center for Control, Dynamical Systems, and Computation, UC Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I4210140143","https://openalex.org/I154570441"]},{"raw_affiliation_string":"Dynamical Systems, and Computation, Center for Control, UC Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I4210140143","https://openalex.org/I154570441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068353454","display_name":"Francesco Bullo","orcid":"https://orcid.org/0000-0002-4785-2118"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]},{"id":"https://openalex.org/I4210140143","display_name":"Dynamic Systems (United States)","ror":"https://ror.org/043vm9914","country_code":"US","type":"company","lineage":["https://openalex.org/I4210140143"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Francesco Bullo","raw_affiliation_strings":["Center for Control, Dynamical Systems, and Computation, UC Santa Barbara, Santa Barbara, CA, USA","Dynamical Systems, and Computation, Center for Control, UC Santa Barbara, Santa Barbara, CA, USA"],"raw_orcid":"https://orcid.org/0000-0002-4785-2118","affiliations":[{"raw_affiliation_string":"Center for Control, Dynamical Systems, and Computation, UC Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I4210140143","https://openalex.org/I154570441"]},{"raw_affiliation_string":"Dynamical Systems, and Computation, Center for Control, UC Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I4210140143","https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5080330764"],"corresponding_institution_ids":["https://openalex.org/I154570441","https://openalex.org/I4210140143"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.20962698,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":null,"first_page":"2853","last_page":"2858"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9926000237464905,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9837999939918518,"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/monotonic-function","display_name":"Monotonic function","score":0.7281314134597778},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6309410333633423},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5773015022277832},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.5532285571098328},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5479585528373718},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4752911329269409},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31998133659362793},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16491231322288513},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.07631245255470276}],"concepts":[{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.7281314134597778},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6309410333633423},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5773015022277832},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.5532285571098328},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5479585528373718},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4752911329269409},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31998133659362793},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16491231322288513},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.07631245255470276},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lcsys.2024.3516632","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcsys.2024.3516632","pdf_url":null,"source":{"id":"https://openalex.org/S4306422535","display_name":"IEEE Control Systems Letters","issn_l":"2475-1456","issn":["2475-1456"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Control Systems Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3055473026","display_name":null,"funder_award_id":"FA9550-21-1-0203","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W205960364","https://openalex.org/W1597286183","https://openalex.org/W1973017038","https://openalex.org/W2002352814","https://openalex.org/W2097113878","https://openalex.org/W2100556411","https://openalex.org/W2133776435","https://openalex.org/W2171505650","https://openalex.org/W2763081248","https://openalex.org/W2789265722","https://openalex.org/W2962717811","https://openalex.org/W2963248893","https://openalex.org/W2964030958","https://openalex.org/W3015406720","https://openalex.org/W3045976650","https://openalex.org/W3097133297","https://openalex.org/W4244393449","https://openalex.org/W4385973814","https://openalex.org/W4395070863","https://openalex.org/W4399146387","https://openalex.org/W6880626306"],"related_works":["https://openalex.org/W2077314575","https://openalex.org/W4315701745","https://openalex.org/W1990290471","https://openalex.org/W4380682190","https://openalex.org/W2005710836","https://openalex.org/W2102386043","https://openalex.org/W2945307361","https://openalex.org/W2116636209","https://openalex.org/W2369988800","https://openalex.org/W4287905284"],"abstract_inverted_index":{"In":[0],"this":[1,67],"letter":[2],"we":[3,30,90,104],"study":[4],"the":[5,33,39,42,57,70,78,86,111],"proximal":[6,43,71,79],"gradient":[7,44],"dynamics.":[8,45],"This":[9],"recently-proposed":[10],"continuous-time":[11],"dynamics":[12],"solves":[13],"optimization":[14,96],"problems":[15,117],"whose":[16],"cost":[17,34,58,87],"functions":[18],"are":[19],"separable":[20],"into":[21],"a":[22,26,49,119,123],"nonsmooth":[23],"convex":[24],"and":[25,64,118],"smooth":[27],"component.":[28],"First,":[29],"show":[31,65,76],"that":[32,52,66,77],"function":[35,59],"decreases":[36],"monotonically":[37],"along":[38],"trajectories":[40],"of":[41,56,85,107],"We":[46,74],"then":[47],"introduce":[48],"new":[50],"condition":[51,68,81],"guarantees":[53,82],"exponential":[54,83],"convergence":[55,84],"to":[60,94],"its":[61],"optimal":[62],"value,":[63],"implies":[69],"Polyak-\u0141ojasiewicz":[72,80],"condition.":[73],"also":[75],"function.":[88],"Moreover,":[89],"extend":[91],"these":[92,108],"results":[93],"time-varying":[95],"problems,":[97],"providing":[98],"bounds":[99],"for":[100],"equilibrium":[101],"tracking.":[102],"Finally,":[103],"discuss":[105],"applications":[106],"findings,":[109],"including":[110],"LASSO":[112],"problem,":[113],"certain":[114],"matrix":[115],"based":[116],"numerical":[120],"experiment":[121],"on":[122],"feed-forward":[124],"neural":[125],"network.":[126]},"counts_by_year":[],"updated_date":"2025-12-27T23:08:20.325037","created_date":"2025-10-10T00:00:00"}
