OPTIMIZATION OF DYNAMICAL-SYSTEMS

Consider an optimization problem where the objective function is an in tegral containing the solution of a system of ordinary differential eq uations. Suppose we have efficient optimization methods available as w ell as efficient methods for initial value problems for ordinary diffe rential equations. The main purpose of this paper is to show how these methods can be efficiently applied to a considered problem. First, th e general procedures for the evaluation of gradients and Hessian matri ces are described. Furthermore, the new efficient Gauss-Newton-like ap proximation of the Hessian matrix is derived for the special case when the objective function is an integral of squares. This approximation is used for deriving the Gauss-Newton-like trust region method, with w hich global and superlinear convergence properties are proved. Finally several optimization methods are proposed and computational experimen ts illustrating their efficiency are shown.