A integral filter algorithm for unconstrained global optimization

In this paper, making use of an integral inequality, a necessary and sufficient condition is given for a point to be a global minimizer. Based on the integral inequality, a novel integral-form algorithm is proposed for unconstrained global optimization. It is different from the other deterministic global search algorithm. Under mild conditions it is proved that, in theory, a global minimizer of the objective function can be certainly found by the presented algorithm. In order to indicate the efficiency and reliability of the method, four numerical examples are reported.