On the approaches to optimization of discontinious functions based on the approximate gradient

The article describes approaches to the discontinuous optimization using the concept of the approximate gradient. The approximate gradient is an integral operator and may be considered as the generalization of the notion of gradient for nondifferential and discontinuous functions. This concept make it possible to generalize the basic theorems of differential calculus and to construct the numerical methods for solving discontinuous extremal problems. The main results of researches fulfilled at the Department of Control Theory and Optimization last years are considered in the article.