A smooth method for the finite minimax problem

The authors consider unconstrained minimax problems where the objective function is the maximum of a finite number of smooth functions. They 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 minimax values. On this basis, the authors can define implementable algorithms for the solution of the minimax problem, which are globally convergent at a superlinear convergence rate. Preliminary numerical results are reported.