Deterministic Algorithm for Global Optimization

A deterministic algorithm for global optimization is presented.The algorithm is one of covering methods which find the global minimum with required degree of accuracy.The principle of the algorithm is region cutting.The regions which the global minimum is not included are found and cut from deeply research.When we research some special functions,we can make a consistent net covering on the region.By calculating the function evaluations of the nodes,the regions in which function evaluation is larger are successively cut and the regions in which function evaluation is smaller are remained.At last,the global minimum is known to the required degree of accuracy.The algorithm requires the bound of the eigenvalues of the Hessian can be estimated and uses the bound to determine the stopping rule.Several numerical examples are presented at the end of the paper.