Pierre Girardeau

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In this paper, we present an Uzawa-based heuristic that is adapted to some type of stochastic optimal control problems. More precisely, we consider dynamical systems that can be divided into small-scale independent subsystems, though linked through a static almost sure coupling constraint at each time step. This type of problem is common in(More)
We prove the almost-sure convergence of a class of sampling-based nested decomposition algorithms for multistage stochastic convex programs in which the stage costs are general convex functions of the decisions , and uncertainty is modelled by a scenario tree. As special cases, our results imply the almost-sure convergence of SDDP, CUPPS and DOASA when(More)
For a sequence of dynamic optimization problems, we aim at discussing a notion of consistency over time. This notion can be informally introduced as follows. At the very first time step t 0 , the decision maker formulates an optimization problem that yields optimal decision rules for all the forthcoming time step t 0 , t 1 ,. .. , T ; at the next time step(More)
We present an algorithm for American option pricing based on stochastic approximation techniques. Option pricing algorithms generally involve some sort of discretization, either on the state space or on the underlying functional space. Our work, which is an application of a more general perturbed gradient algorithm introduced recently by the authors,(More)
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