Interval method for global solutions of a class of min–max–min problems

An interval method for a class of min–max–min problems is described in this paper, in which the objective functions are Lipschitz continuous. The convergence of algorithm is proved, numerical results from a Turbo B implementation of the algorithm are presented. The method can get both the optimal value and all global solutions of min–max–min problem. Theoretical analysis and numerical tests indicate the algorithm is stable and reliable.