In this paper we derive efficiency estimates of the regularized Newton's method as applied to constrained convex minimization problems and to variational inequalities. We study a one-step Newton's method and its multistep accelerated version, which converges on smooth convex problems as O(1/k),...

In this paper we propose two new nonsymmetric primal-dual potential-reduction methods for conic problems. The methods are based on the primal-dual lifting [5]. This procedure allows to construct a strictly feasible primal-dual pair related by an exact scaling relation even if the cones are not...

In this paper we develop a new and efficient method for variational inequality with Lipschitz continuous strongly monotone operator. Our analysis is based on a new strongly convex merit function. We apply a variant of the developed scheme for solving quasivariational inequality. As a result, we...

In this paper we propose new efficient gradient schemes for two non-trivial classes of linear programming problems. These schemes are designed to compute approximate solutions with relative accuracy [delta]. We prove that the upper complexity bound for both schemes is O(([square...

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

In this paper we analyze computational performance of dual trigonometric generating functions on some integer programming problems. We show that if the number of equality constraints is fixed, then this technique allows to solve the problems in time, which is polynomial in the dimension of the...

In this paper we propose an accelerated version of the cubic regularization of Newton's method [6]. The original version, used for minimizing a convex function with Lipschitz - continuous Hessian, guarantees a global rate of convergence of order O(1/k²), where k is the iteration counter. Our...

In many applications it is possible to justify a reasonable bound for possible variation of subgradients of objective function rather than for their uniform magnitude. In this paper we develop a new class of efficient primal-dual subgradient schemes for such problem classes

In this paper, we consider the problem of correlation between the projections of two square matrices. These matrices of dimensions m x m and n x n are projected on a subspace of lower-dimension k under isometry constraints. We maximize the correlation between these projections expressed as a...