Duality in optimal control problems described by convex discrete and differential inclusions (Q1098086)

The Bolza problem for a non-autonomous differential inclusion on a fixed time interval with given initial and terminal convex sets together with a similar problem for a recurrence inclusion is studied. The right-hand- side of these inclusions are convex sets and the integrand and summands in the performance indices are continuous, convex functions. Next, the duals to both previously considered problems are formulated, and under some non-degeneracy condition (similar to the Slater condition) the necessary and sufficient optimality conditions for the dual problems are obtained. At the end some duality theorems are proved.