A Filled Function Method with One Parameter for Box Constraint

In this paper, a new auxiliary function with one parameter for box constraint is proposed. It can escape from the current local minimizer to arrive at a lower local minimizer and can finally go to a global optimal solution. First, a new definition of the filled function for box constrained minimization problem is given, and under mild assumptions, this new auxiliary function can be proved to be a filled function. Then a new solution algorithm is proposed according to the theoretical analysis. And some numerical results demonstrate the efficiency of the proposed algorithm.