The class of nonsmooth codifferentiable functions was introduced by professor V.F.~Demyanov in the late 1980s. He also proposed a method for minimizing these functions called the method of codifferential descent (MCD) that can be applied to various nonsmooth optimization problems. However, until now almost no theoretical results on the performance of this method on particular classes of nonsmooth optimization problems were known. The main goal of this article is to improve our understanding of the MCD and provide a theoretical foundation for the comparison of the MCD with other methods of nonsmooth optimization. In the first part of the paper we study the performance of the method of codifferential descent on a class of nonsmooth convex functions satisfying some regularity assumptions, which in the smooth case are reduced to the Lipschitz continuity of the gradient. We prove that in this case the MCD has the iteration complexity bound $\mathcal{O}(1 / \varepsilon)$. In the second part 查看全文>>