{"id":"https://openalex.org/W4286631413","doi":"https://doi.org/10.1007/s10957-022-02048-5","title":"Proximal Gradient Algorithms Under Local Lipschitz Gradient Continuity","display_name":"Proximal Gradient Algorithms Under Local Lipschitz Gradient Continuity","publication_year":2022,"publication_date":"2022-07-06","ids":{"openalex":"https://openalex.org/W4286631413","doi":"https://doi.org/10.1007/s10957-022-02048-5"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-022-02048-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-022-02048-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-022-02048-5.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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10957-022-02048-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069602662","display_name":"Alberto De Marchi","orcid":"https://orcid.org/0000-0002-3545-6898"},"institutions":[{"id":"https://openalex.org/I40527276","display_name":"Universit\u00e4t der Bundeswehr M\u00fcnchen","ror":"https://ror.org/05kkv3f82","country_code":"DE","type":"education","lineage":["https://openalex.org/I1315109972","https://openalex.org/I40527276","https://openalex.org/I4387152969"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Alberto De Marchi","raw_affiliation_strings":["Department of Aerospace Engineering, Institute of Applied Mathematics and Scientific Computing, Universit\u00e4t der Bundeswehr M\u00fcnchen, Werner-Heisenberg-Weg 39, 85577, Neubiberg, Germany"],"raw_orcid":"https://orcid.org/0000-0002-3545-6898","affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering, Institute of Applied Mathematics and Scientific Computing, Universit\u00e4t der Bundeswehr M\u00fcnchen, Werner-Heisenberg-Weg 39, 85577, Neubiberg, Germany","institution_ids":["https://openalex.org/I40527276"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010064441","display_name":"Andreas Themelis","orcid":"https://orcid.org/0000-0002-6044-0169"},"institutions":[{"id":"https://openalex.org/I135598925","display_name":"Kyushu University","ror":"https://ror.org/00p4k0j84","country_code":"JP","type":"education","lineage":["https://openalex.org/I135598925"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Andreas Themelis","raw_affiliation_strings":["Faculty of Information Science and Electrical Engineering (ISEE), Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan"],"raw_orcid":"https://orcid.org/0000-0002-6044-0169","affiliations":[{"raw_affiliation_string":"Faculty of Information Science and Electrical Engineering (ISEE), Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan","institution_ids":["https://openalex.org/I135598925"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5069602662"],"corresponding_institution_ids":["https://openalex.org/I40527276"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":2.813,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.91324318,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"194","issue":"3","first_page":"771","last_page":"794"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9997000098228455,"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":0.996999979019165,"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"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9944999814033508,"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/proximal-gradient-methods","display_name":"Proximal Gradient Methods","score":0.7710959315299988},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6764207482337952},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.6145867109298706},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6015194654464722},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5792974233627319},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5588341951370239},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5539379715919495},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5445568561553955},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5231698155403137},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.5187745094299316},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5058493614196777},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.49334588646888733},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4215271770954132},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38968557119369507},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14662757515907288},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.0667605996131897},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06639659404754639}],"concepts":[{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.7710959315299988},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6764207482337952},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.6145867109298706},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6015194654464722},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5792974233627319},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5588341951370239},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5539379715919495},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5445568561553955},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5231698155403137},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.5187745094299316},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5058493614196777},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.49334588646888733},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4215271770954132},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38968557119369507},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14662757515907288},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0667605996131897},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06639659404754639},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","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":3,"locations":[{"id":"doi:10.1007/s10957-022-02048-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-022-02048-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-022-02048-5.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:arXiv.org:2112.13000","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2112.13000","pdf_url":"https://arxiv.org/pdf/2112.13000","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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"},{"id":"pmh:oai:RePEc:spr:joptap:v:194:y:2022:i:3:d:10.1007_s10957-022-02048-5","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-022-02048-5","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/s10957-022-02048-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-022-02048-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-022-02048-5.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/G2604714176","display_name":null,"funder_award_id":"JP21K17710.","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4231125181","display_name":"New-generation optimization algorithms for engineering","funder_award_id":"21K17710","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4286631413.pdf","grobid_xml":"https://content.openalex.org/works/W4286631413.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W646582900","https://openalex.org/W1669104078","https://openalex.org/W1946620893","https://openalex.org/W2001732520","https://openalex.org/W2135779729","https://openalex.org/W2466668725","https://openalex.org/W2513710035","https://openalex.org/W2521431955","https://openalex.org/W2535496140","https://openalex.org/W2900403378","https://openalex.org/W2903902823","https://openalex.org/W2950312551","https://openalex.org/W2962688058","https://openalex.org/W2962871487","https://openalex.org/W2963888662","https://openalex.org/W2963967579","https://openalex.org/W3010760670","https://openalex.org/W3021534257","https://openalex.org/W3046485346","https://openalex.org/W3093956689","https://openalex.org/W3101255104","https://openalex.org/W3137344536","https://openalex.org/W3154875414","https://openalex.org/W3155850785","https://openalex.org/W4205339158","https://openalex.org/W4221144244","https://openalex.org/W4230344464","https://openalex.org/W4237231145","https://openalex.org/W4244393449","https://openalex.org/W4249513058","https://openalex.org/W4292073226","https://openalex.org/W4298006464","https://openalex.org/W4302177835","https://openalex.org/W4319459406"],"related_works":["https://openalex.org/W2811217697","https://openalex.org/W4385644471","https://openalex.org/W4320495396","https://openalex.org/W4295266778","https://openalex.org/W2564172750","https://openalex.org/W2041341337","https://openalex.org/W2075334256","https://openalex.org/W2026452100","https://openalex.org/W2372778757","https://openalex.org/W2112655684"],"abstract_inverted_index":{"Abstract":[0],"Composite":[1],"optimization":[2,129],"offers":[3],"a":[4,9,89],"powerful":[5],"modeling":[6],"tool":[7],"for":[8,39,52,98],"variety":[10],"of":[11,20,43,60,75,92,105,122],"applications":[12],"and":[13,94,120,124],"is":[14],"often":[15],"numerically":[16],"solved":[17],"by":[18],"means":[19],"proximal":[21,76,82,107],"gradient":[22,37,83],"methods.":[23],"In":[24],"this":[25],"paper,":[26],"we":[27],"consider":[28],"fully":[29],"nonconvex":[30],"composite":[31],"problems":[32],"under":[33],"only":[34,71],"local":[35],"Lipschitz":[36],"continuity":[38],"the":[40,44,61,72,80,106],"smooth":[41],"part":[42],"objective":[45],"function.":[46],"We":[47],"investigate":[48],"an":[49],"adaptive":[50],"scheme":[51],"PANOC-type":[53],"methods":[54,100],"(Stella":[55],"et":[56],"al.":[57],"in":[58],"Proceedings":[59],"IEEE":[62],"56th":[63],"CDC,":[64],"2017),":[65],"namely":[66],"accelerated":[67,99],"linesearch":[68],"algorithms":[69,93],"requiring":[70],"simple":[73],"oracle":[74],"gradient.":[77],"While":[78],"including":[79],"classical":[81],"method,":[84],"our":[85],"theoretical":[86],"results":[87],"cover":[88],"broader":[90],"class":[91],"provide":[95],"convergence":[96],"guarantees":[97],"with":[101],"possibly":[102,125],"inexact":[103],"computation":[104],"mapping.":[108],"These":[109],"findings":[110],"have":[111],"also":[112],"significant":[113],"practical":[114],"impact,":[115],"as":[116,134],"they":[117],"widen":[118],"scope":[119],"performance":[121],"existing,":[123],"future,":[126],"general":[127],"purpose":[128],"software":[130],"that":[131],"invoke":[132],"PANOC":[133],"inner":[135],"solver.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2022-07-23T00:00:00"}