A Global Regularization Method for Solving the Finite Min-Max Problem

In this paper, we present a method for solving the nite nonlinear min-max problem. By using quasi-Newton methods, we approximately solve a sequence of diierentiable subproblems where, for each subproblem, the cost function to minimize is a global regularization underestimating the nite maximum function. We show that every cluster point of the sequence generated is a stationary point of the min-max problem, and therefore, in the convex case, is a solution of the problem. Moreover, we give numerical results for a large set of test problems which show that the method is eecient in practice.