Minimization of smooth function maxima difference.
The problem of minimizing one class of nonsmooth functions - namely, the functions representing the difference of smooth function maxima is considered. These functions are quasidifferentiable and also continuously codifferentiable. The notion of codifferentiability was introdused by V. F. Demyanov. A necessary condition of a minimum of this difference in terms of functions of such a type are proposed. Conevergence theorems are proved. The examples illustrating the mentioned algorithms are provided.