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dc.contributor.authorLions, Pierre-Louis
dc.contributor.authorSouganidis, Panagiotis E.
dc.date.accessioned2014-05-02T12:48:42Z
dc.date.available2014-05-02T12:48:42Z
dc.date.issued1984
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/13228
dc.language.isoenen
dc.subjectdifferential gamesen
dc.subjectoptimal controlen
dc.subjectHamilton-Jacobi equationsen
dc.subjectdirectional derivativesen
dc.subjectviscosity solutionsen
dc.subject.ddc519en
dc.titleDifferential Games, Optimal Control and Directional Derivatives of Viscosity Solutions of Bellman’s and Isaacs’ Equationsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenRecent work by the authors and others has demonstrated the connections between the dynamic programming approach to optimal control theory and to two-person, zero-sum differential games problems and the new notion of “Viscosity” solutions of Hamilton–Jacobi PDE’s introduced by M. G. Crandall and P.-L. Lions. In particular, it has been proved that the dynamic programming principle implies that the value function is the viscosity solution of the associated Hamilton–Jacobi–Bellman and Isaacs equations. In the present work, it is shown that viscosity super- and subsolutions of these equations must satisfy some inequalities called super- and subdynamic programming principle respectively. This is then used to prove the equivalence between the notion of viscosity solutions and the conditions, introduced by A. Subbotin, concerning the sign of certain generalized directional derivatives.en
dc.relation.isversionofjnlnameSIAM Journal on Control and Optimization
dc.relation.isversionofjnlvol23en
dc.relation.isversionofjnlissue4en
dc.relation.isversionofjnldate1984
dc.relation.isversionofjnlpages566-583en
dc.relation.isversionofdoihttp://dx.doi.org/10.1137/0323036en
dc.relation.isversionofjnlpublisherSIAMen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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