In the paper the existence and continuous dependence of a kind of minimax solution to the dual Hamilton-Jacobi equations is proved. The main difficulties which appear here are a special type of the boundary conditions and the transversality conditions which that solution must satisfy. That type of problems come from optimal control and game theory.

In the present paper, we continue our investigation of optimal control problems for the bidomain equations. In a previous work [ Kunisch/Wagner 11 ] , control problems involving the monodomain approximation of the bidomain system have been considered. Well-posedness of the problem formulation was proved, and first-order optimality conditions were derived. Turning now to the study of optimal con...

For a large class of stochastic processes, the evolution of the underlying probability density function is prescribed by a forward Kolmogorov equation, also called FokkerPlanck equation, a second-order parabolic partial differential equation. In this manner, an optimal control problem subject to an Itô stochastic differential equation can be rendered deterministic by recasting it as an optimal ...

This paper deals with an optimal control problem associated to an evolution implicit quasi-variational inequality for elastic materials. Such problems describe the quasi-static process of bilateral contact with friction between an elastic body and a rigid foundation. Existence of an optimal control is proven and necessary optimality conditions are derived.

We consider a Bolza optimal control problem with state constraints. It is well known that under some technical assumptions every strong local minimizer of this problem satisfies first order necessary optimality conditions in the form of a constrained maximum principle. In general, the maximum principle may be abnormal or even degenerate and so does not provide a sufficient information about opt...

In this paper we study the bilevel dynamic problem, which is a hierarchy of two dynamic optimization problems, where the constraint region of the upper level problem is determined implicitly by the solutions to the lower level optimal control problem. To obtain optimality conditions, we reformulate the bilevel dynamic problem as a single level optimal control problem that involves the value fun...