We have to solve the difficult nonlinear nonconvex constrained global optimization problem (14)-(16), which has a high number of local minima. In order to solve this problem according to our accuracy demands, we propose a two-phase approach. In Phase I, only a rough approximation of a global optimum is computed. This is done with a stochastic optimization method. In Phase II, the previously computed approximation is refined with a highly accurate nonlinear local optimization method. It is well known (Ingber ) that stochastic optimization methods approach very rapidly a global optimum, but converge very slowly once they are in a certain neighbourhood of an optimum. The shunt to another, locally faster method should therefore result in an overall better performance. Our computational results suggests that this is true, at least for the objective function at hand. This is also confirmed by results of Steinacker, Thamm and Maier , who only used a stochastic method to compute a highly accurate approximation to a global optimum. A short survey of other methods which have been proposed to attack this problem is given in .
We also intend to show that there exist optimization codes in the public domain which are comparable in performance with commercial ones. To this end, we decided to use only careful selected free implementations for our computational study.