JNCA: Optimal compatibility problem and its applications



	Volume 10, Number 1, April 2009, pp. 51-72
Elena Rovenskaya
Key words:
Non-convex optimization, numerical algorithms, application to optimal control
Mathematices Subject Classification: Primary 90C26


	Abstract:
	In this paper we consider the problem of finding the minimum value of a scalar parameter at which depending on this parameter an equation has a solution in a given set which also depends on that parameter. A space of arguments is infinite. We call this problem as optimal compatibility problem. Under considered assumptions the optimization problem is not convex. We suggest an iteration method to solving the optimal compatibility problem based on the idea of the method of extremal shifting by N.N.Krasovskiy known in the game theory. We provide an application of the method to solving two classes of optimal control problems.