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dc.contributor.authorGomes, Diogo A.
dc.contributor.authorMitake, Hiroyoshi
dc.contributor.authorTran, Hung V.
dc.date.accessioned2018-02-20T10:38:36Z
dc.date.available2018-02-20T10:38:36Z
dc.date.issued2018-01-26
dc.identifier.citationGOMES DA, MITAKE H, TRAN HV (2018) The selection problem for discounted Hamilton–Jacobi equations: some non-convex cases. Journal of the Mathematical Society of Japan 70: 345–364. Available: http://dx.doi.org/10.2969/jmsj/07017534.
dc.identifier.issn0025-5645
dc.identifier.doi10.2969/jmsj/07017534
dc.identifier.urihttp://hdl.handle.net/10754/627149
dc.description.abstractHere, we study the selection problem for the vanishing discount approximation of non-convex, first-order Hamilton–Jacobi equations. While the selection problem is well understood for convex Hamiltonians, the selection problem for non-convex Hamiltonians has thus far not been studied. We begin our study by examining a generalized discounted Hamilton–Jacobi equation. Next, using an exponential transformation, we apply our methods to strictly quasi-convex and to some non-convex Hamilton–Jacobi equations. Finally, we examine a non-convex Hamiltonian with flat parts to which our results do not directly apply. In this case, we establish the convergence by a direct approach.
dc.publisherMathematical Society of Japan (Project Euclid)
dc.relation.urlhttps://projecteuclid.org/euclid.jmsj/1516957230#info
dc.rightsArchived with thanks to Journal of the Mathematical Society of Japan
dc.subjectDiscounted approximation
dc.subjectErgodic problems
dc.subjectnonconvex Hamilton–Jacobi equations
dc.subjectNonlinear adjoint methods
dc.titleThe selection problem for discounted Hamilton–Jacobi equations: some non-convex cases
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.identifier.journalJournal of the Mathematical Society of Japan
dc.eprint.versionPost-print
dc.contributor.institutionInstitute of Engineering, Division of Electrical Systems and Mathematical Engineering, Hiroshima University, 1-4-1 Kagamiyama Higashi-Hiroshima-shi, Hiroshima, 739-8527, , Japan
dc.contributor.institutionDepartment of Mathematics, University of Wisconsin-Madison, Van Vleck Hall, 480 Lincoln drive, Madison, WI, 53706, , United States
dc.identifier.arxivid1605.07532
kaust.personGomes, Diogo A.
refterms.dateFOA2018-06-14T05:28:02Z
dc.date.published-online2018-01-26
dc.date.published-print2018-01


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