{"id":"https://openalex.org/W7154392433","doi":"https://doi.org/10.48550/arxiv.2604.10191","title":"Policy Iteration for Stationary Discounted Hamilton--Jacobi--Bellman Equations: A Viscosity Approach","display_name":"Policy Iteration for Stationary Discounted Hamilton--Jacobi--Bellman Equations: A Viscosity Approach","publication_year":2026,"publication_date":"2026-04-11","ids":{"openalex":"https://openalex.org/W7154392433","doi":"https://doi.org/10.48550/arxiv.2604.10191"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.10191","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.10191","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.10191","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133618885","display_name":"Namkyeong Cho","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Cho, Namkyeong","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5028468023","display_name":"Yeoneung Kim","orcid":"https://orcid.org/0000-0001-6293-3939"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kim, Yeoneung","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5133618885"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.2935999929904938,"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.2935999929904938,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.2872999906539917,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.11760000139474869,"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/pointwise","display_name":"Pointwise","score":0.7930999994277954},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6855999827384949},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.6366000175476074},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5619000196456909},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5128999948501587},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.45680001378059387},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4323999881744385},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.42980000376701355},{"id":"https://openalex.org/keywords/sigmoid-function","display_name":"Sigmoid function","score":0.41929998993873596},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4129999876022339}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.7930999994277954},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7810999751091003},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6855999827384949},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.6366000175476074},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5619000196456909},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5372999906539917},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5128999948501587},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.45680001378059387},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4323999881744385},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.42980000376701355},{"id":"https://openalex.org/C81388566","wikidata":"https://www.wikidata.org/wiki/Q526668","display_name":"Sigmoid function","level":3,"score":0.41929998993873596},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4129999876022339},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.3806000053882599},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3785000145435333},{"id":"https://openalex.org/C71287196","wikidata":"https://www.wikidata.org/wiki/Q847204","display_name":"Limit of a sequence","level":3,"score":0.37779998779296875},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.36469998955726624},{"id":"https://openalex.org/C12715386","wikidata":"https://www.wikidata.org/wiki/Q7624691","display_name":"Strongly monotone","level":3,"score":0.362199991941452},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.3571000099182129},{"id":"https://openalex.org/C27156116","wikidata":"https://www.wikidata.org/wiki/Q1778098","display_name":"Pointwise convergence","level":3,"score":0.3560999929904938},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3472999930381775},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.34439998865127563},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3366999924182892},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3237000107765198},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3127000033855438},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3059999942779541},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3052000105381012},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.2987000048160553},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.2980000078678131},{"id":"https://openalex.org/C127172972","wikidata":"https://www.wikidata.org/wiki/Q128709","display_name":"Viscosity","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C196267783","wikidata":"https://www.wikidata.org/wiki/Q4392490","display_name":"Resolvent","level":2,"score":0.2806999981403351},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.2782999873161316},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.2741999924182892},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.26260000467300415},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2547999918460846}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.10191","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.10191","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.10191","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.10191","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,62,151],"study":[1],"policy":[2,99,171],"iteration":[3,172,182],"(PI)":[4],"for":[5,45,68],"deterministic":[6],"infinite-horizon":[7],"discounted":[8,71,149],"optimal":[9],"control":[10,194],"problems,":[11],"whose":[12],"value":[13],"function":[14],"is":[15,28,41,141],"characterized":[16],"by":[17,73,143],"a":[18,58,64,75,96,107,165,178],"stationary":[19,70],"Hamilton--Jacobi--Bellman":[20],"(HJB)":[21],"equation.":[22],"At":[23],"the":[24,31,50,69,91,113,125,134,139,144,148,154,197,204,209],"PDE":[25],"level,":[26],"PI":[27,127],"fundamentally":[29,110],"ill-posed:":[30],"improvement":[32,100],"step":[33],"requires":[34],"pointwise":[35,98],"evaluation":[36],"of":[37,81,90,147,208],"$\\nabla":[38],"V$,":[39],"which":[40],"not":[42],"well":[43],"defined":[44],"viscosity":[46,80],"solutions,":[47],"and":[48,94,131,163,184,192,203],"thus":[49],"associated":[51],"nonlinear":[52,190],"operator":[53],"cannot":[54],"be":[55],"interpreted":[56],"in":[57,189],"stable":[59],"functional":[60],"sense.":[61],"develop":[63],"monotone":[65],"semi-discrete":[66,126],"formulation":[67],"setting":[72],"introducing":[74],"space-discrete":[76],"scheme":[77],"with":[78],"artificial":[79],"order":[82],"$O(h)$.":[83],"This":[84],"regularization":[85],"restores":[86],"comparison,":[87],"ensures":[88],"monotonicity":[89],"discrete":[92,102,136],"operator,":[93],"yields":[95],"well-defined":[97],"via":[101],"gradients.":[103],"Our":[104],"analysis":[105],"reveals":[106],"convergence":[108,202],"mechanism":[109],"different":[111],"from":[112,174],"finite-horizon":[114],"case.":[115],"For":[116],"each":[117],"fixed":[118],"mesh":[119,185],"size":[120],"$h>0$,":[121],"we":[122],"prove":[123],"that":[124,169],"sequence":[128],"converges":[129],"monotonically":[130],"geometrically":[132],"to":[133],"unique":[135],"solution,":[137],"where":[138],"contraction":[140],"induced":[142],"resolvent":[145],"structure":[146],"operator.":[150],"further":[152],"establish":[153],"sharp":[155],"vanishing-viscosity":[156],"estimate":[157],"$\\|V^h":[158],"-":[159],"V\\|_{L^\\infty}":[160],"\\leq":[161],"C\\sqrt{h}$,":[162],"derive":[164],"quantitative":[166],"error":[167,173],"decomposition":[168],"separates":[170],"discretization":[175],"error,":[176],"exhibiting":[177],"nontrivial":[179],"coupling":[180],"between":[181],"count":[183],"size.":[186],"Numerical":[187],"experiments":[188],"one":[191],"two-dimensional":[193],"problems":[195],"confirm":[196],"theoretical":[198],"predictions,":[199],"including":[200],"geometric":[201],"characteristic":[205],"decay-then-plateau":[206],"behavior":[207],"total":[210],"error.":[211]},"counts_by_year":[],"updated_date":"2026-04-15T06:04:33.058270","created_date":"2026-04-15T00:00:00"}