Application of the hypodifferential descent method to the problem of constructing an optimal control

In this paper the problem of optimal control in the classical statement is considered. With the help of the theory of exact penalty functions the original problem is reduced to the problem of unconstrained minimization of a nonsmooth functional. For this functional the necessary minimum conditions in terms of hypodifferential are found. A class of problems, for which these conditions are also sufficient, is distinguished. On the basis of these conditions the hypodifferential descent method is applied to the considered problem. Under some additional assumptions the hypodifferential descent method converges in a certain sense.