On the convergence of an iterative method for the minimax problem

In this paper we present an Extended Linear-Quadratic Programming method for the minimax problem. We show that the Extended Linear-Quadratic Programming method for the minimax problem is equivalent to the Josephy-Newton method for generalized equation, and establish the local convergence result. Furthermore, we obtain the global convergence result for the minimax problem by means of the equivalence relation between the generalized equation and the normal equation.