Stochastic Optimal Control and Linear Programming Approach

Journal Article · Fri Apr 15 00:00:00 EDT 2011 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-010-9120-Y· OSTI ID:22043932

Buckdahn, R ^[1]; Goreac, D ^[2]; Quincampoix, M ^[1]

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1. Universite de Bretagne Occidentale, Laboratoire de Mathematiques, unite CNRS 6205 (France)
2. Laboratoire d'Analyse et de Mathematiques Appliquees, Universite Paris-Est Marne-la-Vallee (France)

We study a classical stochastic optimal control problem with constraints and discounted payoff in an infinite horizon setting. The main result of the present paper lies in the fact that this optimal control problem is shown to have the same value as a linear optimization problem stated on some appropriate space of probability measures. This enables one to derive a dual formulation that appears to be strongly connected to the notion of (viscosity sub) solution to a suitable Hamilton-Jacobi-Bellman equation. We also discuss relation with long-time average problems.

• OSTI ID: 22043932
• Journal Information: Applied Mathematics and Optimization, Vol. 63, Issue 2; Other Information: Copyright (c) 2011 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
HAMILTON-JACOBI EQUATIONS
LINEAR PROGRAMMING
MATHEMATICAL SOLUTIONS
OPTIMAL CONTROL
OPTIMIZATION
PROBABILITY
SPACE
STOCHASTIC PROCESSES