{"title":"On classical solutions and canonical transformations for Hamilton–Jacobi–Bellman equations","authors":"Mohit Bansil, Alpár R. Mészáros","doi":"10.1112/blms.70078","DOIUrl":null,"url":null,"abstract":"<p>In this note, we show how canonical transformations reveal hidden convexity properties for deterministic optimal control problems, which in turn result in global existence of <span></span><math>\n <semantics>\n <msubsup>\n <mi>C</mi>\n <mrow>\n <mi>l</mi>\n <mi>o</mi>\n <mi>c</mi>\n </mrow>\n <mrow>\n <mn>1</mn>\n <mo>,</mo>\n <mn>1</mn>\n </mrow>\n </msubsup>\n <annotation>$C^{1,1}_{loc}$</annotation>\n </semantics></math> solutions to first-order Hamilton–Jacobi–Bellman equations.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 7","pages":"2045-2057"},"PeriodicalIF":0.9000,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70078","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/blms.70078","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this note, we show how canonical transformations reveal hidden convexity properties for deterministic optimal control problems, which in turn result in global existence of solutions to first-order Hamilton–Jacobi–Bellman equations.