SMOOTH TRANSFORMATION OF THE GENERALIZED MINIMAX PROBLEM

We consider the generalized minimax problem, that is, the problem of m inimizing a function phi (x) = F(g(l)(x),...,g(m) (x)), where F is a s mooth function and each g(i) is the maximum of a finite number of smoo th functions. We prove that, under suitable assumptions, it is possibl e to construct a continuously differentiable exact barrier function, w hose minimizers yield the minimizers of the function phi. In this way, the nonsmooth original problem can be solved by usual minimization te chniques for unconstrained differentiable functions.