Transformation Function Method for Unconstrained Global Optimization

In order to find global minimizer, a transformation function without any parameters is proposed for solving unconstrained global optimization problems. This transformation function method is based on a similar idea to the filled function method. The properties of the transformation function are discussed in the region where the objective function values are not higher than the obtained minimum. Based on these properties, we can determine whether or not the current local minimizer is the global minimizer. An algorithm for unconstrained global optimization is developed from this transformation function.