First and second order necessary conditions for stochastic optimal control problems

Joseph Frédéric Bonnans 1, 2 Francisco Silva 3
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
Abstract : In this work we consider a stochastic optimal control problem with either convex control constraints or finitely many equality and inequality constraints over the final state. Using the variational approach, we are able to obtain first and second order expansions for the state and cost function, around a local minimum. This fact allows us to prove general first order necessary condition and, under a geometrical assumption over the constraint set, second order necessary conditions are also established. We end by giving second order optimality conditions for problems with constraints on expectations of the final state.
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Applied Mathematics and Optimization, Springer Verlag (Germany), 2012, 65 (3), pp.403-439
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Joseph Frédéric Bonnans, Francisco Silva. First and second order necessary conditions for stochastic optimal control problems. Applied Mathematics and Optimization, Springer Verlag (Germany), 2012, 65 (3), pp.403-439. 〈inria-00537227v2〉

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