In this paper we analyze several new methods for solving optimization problems with the objective function formed as a sum of two convex terms: one is smooth and given by a black-box oracle, and another is general but simple and its structure is known. Despite to the bad properties of the sum,...

In this paper we propose a new approach for constructing efficient schemes for nonsmooth convex optimization. It is based on a special smoothing technique, which can be applied to the functions with explicit max-structure. Our approach can be considered as an alternative to black-box...

In this paper we extend the smoothing technique [7], [9] onto the problems of Semidefinite Optimization. For that, we develop a simple framework for estimating a Lipschitz constant for the gradient of some symmetric functions of eigenvalues of symmetric matrices. Using this technique, we can...

In this paper we study the Riemannian length of the primal central path computed with respect to the local metric defined by a self-concordant function. We show that despite to some examples, in many important situations the length of this path is quite close to the length of geodesic curves. We...

In this paper we introduce a new primal-dual technique for convergence analysis of gradient schemes for non-smooth convex optimization. As an example of its application, we derive a primal-dual gradient method for a special class of structured non-smooth optimization problems, which ensures a...