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

A method is presented for solving the finite nonlinear min-max problem. Quasi-Newton methods are used to approximately solve a sequence of differentiable subproblems where, for each subproblem, the cost function to minimize is a global regularization underestimating the finite maximum function. Every cluster point of the sequence generated is shown to be a stationary point of the min-max problem and therefore, in the convex case, to be a solution of the problem. Moreover, numerical results are given for a large set of test problems which show that the method is efficient in practice.