In this paper, we present new methods for black-box convex minimization. They do not need to know in advance the actual level of smoothness of the objective function. The only essential input parameter is the required accuracy of the solution. At the same time, for each particular problem class...

In this paper we develop a new primal-dual subgradient method for nonsmooth convex optimization problems. This scheme is based on a self-concordant barrier for the basic feasible set. It is suitable for finding approximate solutions with certain relative accuracy. We discuss some applications of...

In this paper we present a new approach for constructing subgradient schemes for different types of nonsmooth problems with convex structure. Our methods are primaldual since they are always able to generate a feasible approximation to the optimum of an appropriately formulated dual problem....