A hybrid algorithm for finding a global minimum

One of the most important problems in non-linear programming is to find out the global minimum of a given objective function. In this paper, a new hybrid algorithm which combines the random optimization method of Matyas (1965) and one of the well-known ordinary descent algorithms having an effective convergence property (for example, the Fletcher-Reeves conjugate gradient method, the Davidon-Fletcher-Powell quasi Newton method, etc.) is proposed in order to find out a global minimum in as small a number of steps as possible. Several computational experiments on multimodal objective functions are carried out in order to test the efficiency of the proposed hybrid algorithm. The results obtained imply that the proposed hybrid algorithm is useful for finding out a global minimum in a small number of steps. A theorem that predicts convergence to a global minimum is also given.