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

Frédéric Bonnans 1, 2 Justina Gianatti 3 Francisco José Silva 4
1 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR7641
4 XLIM-DMI - DMI
XLIM - XLIM
Abstract : 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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Mathematical Control and Related Fields, AIMS, 2016, 〈10.3934/mcrf.2016008〉
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Contributeur : Francisco José Silva <>
Soumis le : lundi 28 décembre 2015 - 06:10:49
Dernière modification le : jeudi 11 janvier 2018 - 06:26:29

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

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