A filled function method with one parameter for box constrained global optimization

In this paper, a new auxiliary function with one parameter on box constrained for escaping the current local minimizer of global optimization problem is proposed. First, a new definition of the filled function for box constrained minimization problem is given and under mild assumptions, this new auxiliary function is really a filled function. Then a new solution algorithm is proposed according to the theoretical analysis. And some numerical results demonstrate the efficiency of this method for box constrained global optimization.