The method of feasible directions for minimax problems

A general concept of converging algorithms of feasible direction type is introduced using upper approximation functions of the objective. By this means the zigzagging effect can be avoided and convergence to inf-stationary points of the objective is proved. The concept works both in unconstrained and in the regular constrained case of minimizing directionally differentiable functions. For the minimization problem of discrete and continuous maximum functions the algorithm will be formulated explicitly, and the practical realization of the sub-problems will be discussed.