A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality theorems are proved. The dual problem serves to provide upper bounds for the optimal and maximum value of the original one or even to give the optimal value.
Nonconvex penalization of switching control of partial differential equations
Change of Optimal Values: A Pre-calculated Metric
Another Look at Partially Observed Optimal Stochastic Control: Existence, Ergodicity, and Approximations without Belief-Reduction
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