{"id":"https://openalex.org/W1985662043","doi":"https://doi.org/10.1137/070705465","title":"Policy Iteration and the Max-Plus Finite Element Method","display_name":"Policy Iteration and the Max-Plus Finite Element Method","publication_year":2008,"publication_date":"2008-12-05","ids":{"openalex":"https://openalex.org/W1985662043","doi":"https://doi.org/10.1137/070705465","mag":"1985662043"},"language":"en","primary_location":{"id":"doi:10.1137/070705465","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070705465","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","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/A5043885180","display_name":"David P. McCaffrey","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"D. McCaffrey","raw_affiliation_strings":["david@mccaffrey275.fsnet.co.uk#TAB#"],"affiliations":[{"raw_affiliation_string":"david@mccaffrey275.fsnet.co.uk#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5043885180"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.05183127,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"47","issue":"6","first_page":"2912","last_page":"2929"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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":0.9939000010490417,"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9926999807357788,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8344767093658447},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5998427271842957},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5884162187576294},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5118278861045837},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.4966455101966858},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4958244264125824},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.45013323426246643},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.44285720586776733},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4226389229297638},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4205150008201599},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39285558462142944},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25305330753326416},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10016238689422607},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08444935083389282}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8344767093658447},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5998427271842957},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5884162187576294},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5118278861045837},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.4966455101966858},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4958244264125824},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.45013323426246643},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.44285720586776733},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4226389229297638},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4205150008201599},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39285558462142944},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25305330753326416},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10016238689422607},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08444935083389282},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/070705465","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070705465","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1969186802","https://openalex.org/W1970266193","https://openalex.org/W1991917939","https://openalex.org/W2034750182","https://openalex.org/W2043228814","https://openalex.org/W2106758919","https://openalex.org/W2109640889","https://openalex.org/W2113350382","https://openalex.org/W2156268532"],"related_works":["https://openalex.org/W2038416447","https://openalex.org/W2364151838","https://openalex.org/W2066926363","https://openalex.org/W2354159744","https://openalex.org/W2030549801","https://openalex.org/W2351539857","https://openalex.org/W2381972071","https://openalex.org/W4301382669","https://openalex.org/W4387635768","https://openalex.org/W4389116212"],"abstract_inverted_index":{"We":[0,82],"set":[1],"out":[2],"a":[3,11,23,31,89],"policy":[4,54,69,76],"iteration":[5],"algorithm":[6,86],"for":[7],"the":[8,20,37,42,49,53,56,68,74,79,85,96],"solution":[9],"of":[10,22,41,51,55,92,102],"nonconvex":[12],"nonlinear-affine":[13],"finite":[14,25,90],"horizon":[15],"differential":[16],"game.":[17],"This":[18],"involves":[19],"use":[21],"max-plus":[24],"element":[26],"method":[27],"(FEM)":[28],"to":[29,72],"solve":[30],"convex":[32,46],"optimal":[33],"control":[34],"problem":[35,47],"in":[36,67,88],"value":[38],"determination":[39],"step":[40,71],"algorithm,":[43],"where":[44],"this":[45],"is":[48,64,101],"result":[50],"fixing":[52],"second,":[57],"or":[58],"outer,":[59],"player.":[60,81],"A":[61],"quadratic":[62],"program":[63],"then":[65],"solved":[66],"improvement":[70],"improve":[73],"feedback":[75],"employed":[77],"by":[78],"outer":[80],"show":[83],"that":[84,95],"converges":[87],"number":[91],"steps":[93],"and":[94],"approximation":[97],"error":[98],"at":[99],"convergence":[100],"order":[103],"$\\sqrt{\\Delta":[104],"t}+\\Delta":[105],"x(\\Delta":[106],"t)^{-1}$.":[107]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
