Stochastic Optimal Control and Linear Programming Approach

Rainer Buckdahn (1, 2) , Dan Goreac (3) , Marc Quincampoix (1)

1 LM - Laboratoire de mathématiques de Brest
2 Institute for Advanced Study Jinan
3 PS

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.

Mots clés: Linear programming; Stochastic control under constraints; Occupational measures; Viscosity solutions; Long-time averaging

Domaines: Optimisation et contrôle [math.OC]; Probabilités [math.PR]; Equations aux dérivées partielles [math.AP]

Rainer Buckdahn, Dan Goreac, Marc Quincampoix. Stochastic Optimal Control and Linear Programming Approach. Applied Mathematics and Optimization, 2011, 63 (2), pp.257-276. ⟨10.1007/s00245-010-9120-y⟩. ⟨hal-00727715⟩