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Weak Dynamic Programming for Generalized State Constraints

Abstract : We provide a dynamic programming principle for stochastic optimal control problems with expectation constraints. A weak formulation, using test functions and a probabilistic relaxation of the constraint, avoids restrictions related to a measurable selection but still implies the Hamilton-Jacobi-Bellman equation in the viscosity sense. We treat open state constraints as a special case of expectation constraints and prove a comparison theorem to obtain the equation for closed state constraints.
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Contributor : Bruno Bouchard <>
Submitted on : Thursday, May 5, 2011 - 1:10:08 PM
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Bruno Bouchard, Marcel Nutz. Weak Dynamic Programming for Generalized State Constraints. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2012, 50 (6), pp.3344-3373. ⟨10.1137/110852942⟩. ⟨hal-00590874⟩

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