{"id":"https://openalex.org/W4221146748","doi":"https://doi.org/10.1109/lcsys.2022.3181213","title":"Dynamic Programming Through the Lens of Semismooth Newton-Type Methods","display_name":"Dynamic Programming Through the Lens of Semismooth Newton-Type Methods","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4221146748","doi":"https://doi.org/10.1109/lcsys.2022.3181213"},"language":"en","primary_location":{"id":"doi:10.1109/lcsys.2022.3181213","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcsys.2022.3181213","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","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/20.500.11850/558296","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091908459","display_name":"Matilde Gargiani","orcid":"https://orcid.org/0000-0001-8615-6214"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Gargiani","raw_affiliation_strings":["Automatic Control Laboratory, ETH Z&#x00FC;rich, Z&#x00FC;rich, Switzerland"],"raw_orcid":"https://orcid.org/0000-0001-8615-6214","affiliations":[{"raw_affiliation_string":"Automatic Control Laboratory, ETH Z&#x00FC;rich, Z&#x00FC;rich, Switzerland","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040892104","display_name":"Andrea Zanelli","orcid":"https://orcid.org/0000-0003-3525-0686"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. Zanelli","raw_affiliation_strings":["Institute for Dynamic Systems and Control, ETH Z&#x00FC;rich, Z&#x00FC;rich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Dynamic Systems and Control, ETH Z&#x00FC;rich, Z&#x00FC;rich, Switzerland","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042996410","display_name":"Dominic Liao-McPherson","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D. Liao-McPherson","raw_affiliation_strings":["Automatic Control Laboratory, ETH Z&#x00FC;rich, Z&#x00FC;rich, Switzerland"],"raw_orcid":"https://orcid.org/0000-0002-5675-5635","affiliations":[{"raw_affiliation_string":"Automatic Control Laboratory, ETH Z&#x00FC;rich, Z&#x00FC;rich, Switzerland","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051772147","display_name":"Tyler Summers","orcid":"https://orcid.org/0000-0002-0113-8912"},"institutions":[{"id":"https://openalex.org/I162577319","display_name":"The University of Texas at Dallas","ror":"https://ror.org/049emcs32","country_code":"US","type":"education","lineage":["https://openalex.org/I162577319"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"T. H. Summers","raw_affiliation_strings":["Department of Mechanical Engineering, University of Texas at Dallas, Richardson, TX, USA"],"raw_orcid":"https://orcid.org/0000-0002-0113-8912","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of Texas at Dallas, Richardson, TX, USA","institution_ids":["https://openalex.org/I162577319"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007359599","display_name":"John Lygeros","orcid":"https://orcid.org/0000-0002-6159-1962"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Lygeros","raw_affiliation_strings":["Automatic Control Laboratory, ETH Z&#x00FC;rich, Z&#x00FC;rich, Switzerland"],"raw_orcid":"https://orcid.org/0000-0002-6159-1962","affiliations":[{"raw_affiliation_string":"Automatic Control Laboratory, ETH Z&#x00FC;rich, Z&#x00FC;rich, Switzerland","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0867331,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"6","issue":null,"first_page":"2996","last_page":"3001"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13497","display_name":"Hermeneutics and Narrative Identity","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/1211","display_name":"Philosophy"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T13497","display_name":"Hermeneutics and Narrative Identity","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/1211","display_name":"Philosophy"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T13695","display_name":"Aging, Elder Care, and Social Issues","score":0.9749000072479248,"subfield":{"id":"https://openalex.org/subfields/3600","display_name":"General Health Professions"},"field":{"id":"https://openalex.org/fields/36","display_name":"Health Professions"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T13099","display_name":"Health, Medicine and Society","score":0.95660001039505,"subfield":{"id":"https://openalex.org/subfields/3600","display_name":"General Health Professions"},"field":{"id":"https://openalex.org/fields/36","display_name":"Health Professions"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/markov-decision-process","display_name":"Markov decision process","score":0.8655188083648682},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6285203099250793},{"id":"https://openalex.org/keywords/fixed-point-iteration","display_name":"Fixed-point iteration","score":0.6269469261169434},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.6150124073028564},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.547662079334259},{"id":"https://openalex.org/keywords/power-iteration","display_name":"Power iteration","score":0.547185480594635},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5460491180419922},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.5457642674446106},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.5235393047332764},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.520262598991394},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49840664863586426},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.4852852523326874},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4222908020019531},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41968581080436707},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.41434842348098755},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.3223453462123871},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.2736437916755676},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.09624668955802917},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08416357636451721},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.06967902183532715}],"concepts":[{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.8655188083648682},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6285203099250793},{"id":"https://openalex.org/C157449380","wikidata":"https://www.wikidata.org/wiki/Q1030759","display_name":"Fixed-point iteration","level":3,"score":0.6269469261169434},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.6150124073028564},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.547662079334259},{"id":"https://openalex.org/C162443888","wikidata":"https://www.wikidata.org/wiki/Q1426504","display_name":"Power iteration","level":3,"score":0.547185480594635},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5460491180419922},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.5457642674446106},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.5235393047332764},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.520262598991394},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49840664863586426},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.4852852523326874},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4222908020019531},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41968581080436707},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.41434842348098755},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3223453462123871},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.2736437916755676},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.09624668955802917},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08416357636451721},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.06967902183532715},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/lcsys.2022.3181213","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcsys.2022.3181213","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"},{"id":"pmh:oai:www.research-collection.ethz.ch:20.500.11850/558296","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/558296","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Control Systems Letters, 6","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.3929/ethz-b-000558296","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000558296","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:www.research-collection.ethz.ch:20.500.11850/558296","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/558296","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Control Systems Letters, 6","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7556574079","display_name":null,"funder_award_id":"787845 (OCAL)","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W388179047","https://openalex.org/W1551360398","https://openalex.org/W2036742156","https://openalex.org/W2042680115","https://openalex.org/W2048564717","https://openalex.org/W2061508005","https://openalex.org/W2066538609","https://openalex.org/W2257979135","https://openalex.org/W4206956014","https://openalex.org/W4285292047","https://openalex.org/W6660459066","https://openalex.org/W6801946661"],"related_works":["https://openalex.org/W1819217","https://openalex.org/W10321360","https://openalex.org/W11287410","https://openalex.org/W10036223","https://openalex.org/W4199186","https://openalex.org/W6835340","https://openalex.org/W6639212","https://openalex.org/W10944451","https://openalex.org/W11872475","https://openalex.org/W6215125"],"abstract_inverted_index":{"Policy":[0],"iteration":[1,4,46,82,106,113,124],"and":[2,22,55,75,115,129],"value":[3,105,123],"are":[5,29],"at":[6],"the":[7,37,50,71,111],"core":[8],"of":[9,31,73,94,98,110,122],"many":[10],"(approximate)":[11],"dynamic":[12],"programming":[13],"methods.":[14],"For":[15],"Markov":[16],"Decision":[17],"Processes":[18],"with":[19,125],"finite":[20],"state":[21],"action":[23],"spaces,":[24],"we":[25,42],"show":[26,103],"that":[27,44,80,104],"they":[28],"instances":[30],"semismooth":[32,52],"Newton-type":[33],"methods":[34],"for":[35],"solving":[36],"Bellman":[38],"equation.":[39],"In":[40],"particular,":[41],"prove":[43],"policy":[45,81],"is":[47,64,107],"equivalent":[48],"to":[49,88],"exact":[51],"Newton":[53],"method":[54,114],"enjoys":[56],"a":[57,95,117],"local":[58],"quadratic":[59],"convergence":[60,90,127],"rate.":[61],"This":[62],"finding":[63],"corroborated":[65],"by":[66],"extensive":[67],"numerical":[68],"evidence":[69],"in":[70,92],"fields":[72],"control":[74],"operations":[76],"research,":[77],"which":[78],"confirms":[79],"generally":[83],"requires":[84],"relatively":[85],"few":[86],"iterations":[87],"achieve":[89],"even":[91],"presence":[93],"large":[96],"number":[97],"admissible":[99],"policies.":[100],"We":[101],"then":[102],"an":[108],"instance":[109],"fixed-point":[112],"develop":[116],"novel":[118],"locally":[119],"accelerated":[120],"version":[121],"global":[126],"guarantees":[128],"negligible":[130],"extra":[131],"computational":[132],"costs.":[133]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2022-04-03T00:00:00"}
