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Article Dans Une Revue Mathematical Control and Related Fields Année : 2016

On the convergence of the Sakawa-Shindo algorithm in stochastic control

Résumé

We analyze an algorithm for solving stochastic control problems, based on Pontryagin's maximum principle, due to Sakawa and Shindo in the deterministic case and extended to the stochastic setting by Mazliak. We assume that either the volatility is an affine function of the state, or the dynamics are linear. We obtain a monotone decrease of the cost functions as well as, in the convex case, the fact that the sequence of controls is minimizing, and converges to an optimal solution if it is bounded. In a specific case we interpret the algorithm as the gradient plus projection method and obtain a linear convergence rate to the solution.
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Dates et versions

hal-01148272 , version 1 (04-05-2015)
hal-01148272 , version 2 (28-12-2015)

Licence

Paternité - Pas d'utilisation commerciale - Pas de modification

Identifiants

Citer

Frédéric J. Bonnans, Justina Gianatti, Francisco José Silva. On the convergence of the Sakawa-Shindo algorithm in stochastic control. Mathematical Control and Related Fields, 2016, ⟨10.3934/mcrf.2016008⟩. ⟨hal-01148272v2⟩
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