A SMOOTH METHOD FOR THE FINITE MINIMAX PROBLEM

We consider unconstrained minimax problems where the objective functio n is the maximum of a finite number of smooth functions. We prove that , under usual assumptions, it is possible to construct a continuously differentiable function, whose minimizers yield the minimizers of the max function and the corresponding minimum values. On this basis, we c an define implementable algorithms for the solution of the minimax pro blem, which are globally convergent at a superlinear convergence rate. Preliminary numerical results are reported.