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Discontinuous control problems with state constraints : Linear formulations and dynamic programming principles

Dan Goreac 1 Carina Ivascu 2
1 PS
LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
Abstract : This paper aims at studying a class of discontinuous deterministic control problems under state constraints using a linear programming approach. As for classical control problems (Gaitsgory and Quincampoix (2009), Goreac and Serea (2011)), the primal linear problem is stated on some appropriate space of probability measures. Naturally, the support of these measures is contained in the set of constraints. This linearized value function and its dual can, alternatively, be seen as the limit of standard penalized problems. Second, we provide a semigroup property for this set of probability measures leading to dynamic programming principles for control problems under state constraints. An abstract principle is provided for general bounded costs. Linearized versions are obtained under further (semi)continuity assumptions.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00793574
Contributor : Dan Goreac <>
Submitted on : Friday, February 22, 2013 - 3:35:40 PM
Last modification on : Thursday, March 19, 2020 - 12:26:03 PM

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Dan Goreac, Carina Ivascu. Discontinuous control problems with state constraints : Linear formulations and dynamic programming principles. Journal of Mathematical Analysis and Applications, Elsevier, 2013, 402 (2), pp.635--647. ⟨10.1016/j.jmaa.2012.12.043⟩. ⟨hal-00793574⟩

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