A spline smoothing Newton method for finite minimax problems

A spline smoothing stabilized Newton method for finite minimax problems is developed. The spline smoothing technique uses a smooth cubic spline instead of a max function, and, at any fixed point, only a few components of the max function are involved; i.e., it introduces an active set technique, so the proposed method is more efficient for minimizing the maximum function of a large number of complicated functions. Some numerical results comparisons with other methods are also given to show the efficiency of the new method.