Adaptive methods for solving minimax problems

We consider finite-dimensional minimax problems for two traditional models: firstly, with box constraints at variables and, secondly, taking into account a finite number of linear inequalities. We present finite exact primal and dual methods. These methods are adapted to a great extent to the specific structure of the cost function which is formed by a finite number of linear functions. During the iterations of the primal method we make use of the information from the dual problem, thereby increasing effectiveness. To improve the dual method we use the "long dual step" rule (the principle of full relaxation). The results are illustrated by numerical experiments.