Feedback Functions in Problems Minimax Search

This paper considers a method for obtaining a smooth approximation of the maximum function. Some generalizations of this approach are suggested, including formulas for minimax, maximin and their combinations. The resulting error is estimated and ways to reduce it are indicated. The proposed method uses functions that establish feedback links between primary and dual variables of the Lagrange function. These links are similar to the Karush-Kuhn-Tucker theorem, but without conditions of non-negativity or complementary non-rigidity. To illustrate the proposed method, task of searching for global extremum, estimation of the minimax value and an example from game theory are considered.