Convex duality and generalized solutions in the optimal control problem for stopped processes-the deterministic model

The approach consists of imbedding the original control problem tightly in a convex mathematical programming problem on the space of measures and then solving the latter problem by duality in convex analysis. The dual problem is to find the supremum of all smooth subsolutions to Bellman´s equation. Because of the effect of stops at the boundary of the domain, a different formulation of strong and weak problems is adopted to make use of the duality method. Results on the decomposition of weak measures provide a clear interpretation for such an effect in the weak formulation of the control problem. The convex duality approach of W.H. Fleming and D. Vermes (1989) is used to study a deterministic optimal control problem for stopped processes