This paper presents a new method for solving global optimization problems. We use a local technique based on the notion of discrete gradients for finding a cone of descent directions and then we use a global cutting angle algorithm for finding global minimum within the intersection of the cone and the feasible region. We present results of numerical experiments with well-known test problems and with the so-called cluster function. These results confirm that the proposed algorithm allows one to find a global minimizer or at least a deep local minimizer of a function with a huge amount of shallow local minima.
Centre for Informatics and Applied Optimization, School of Information Technology and Mathematical Sciences, University of Ballarat, Victoria 3353, Australia, December 2003