First and Second Order Necessary Conditions for Stochastic Optimal Control Problems

Journal Article · Fri Jun 15 00:00:00 EDT 2012 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-012-9162-4· OSTI ID:22043760

Bonnans, J. Frederic, E-mail: [e-mail] ^[1]; Silva, Francisco J., E-mail: [e-mail] ^[2]

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1. Ecole Polytechnique, INRIA-Saclay and CMAP (France)
2. Dipartimento di Matematica Guido Castelnuovo (Italy)

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.

• OSTI ID: 22043760
• Journal Information: Applied Mathematics and Optimization, Vol. 65, Issue 3; Other Information: Copyright (c) 2012 Springer Science+Business Media, LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
FUNCTIONS
GEOMETRY
MATHEMATICAL SOLUTIONS
OPTIMAL CONTROL
STOCHASTIC PROCESSES
VARIATIONAL METHODS