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Contracting Proximal Methods for Smooth Convex Optimization
TLDR
We propose new accelerated methods for smooth Convex Optimization, called Contracting Proximal Methods. Expand
Randomized Block Cubic Newton Method
TLDR
We study the problem of minimizing the sum of three convex functions: a differentiable, twice-differentiable and a non-smooth term in a high dimensional setting. Expand
Local convergence of tensor methods
In this paper, we study local convergence of high-order Tensor Methods for solving convex optimization problems with composite objective. We justify local superlinear convergence under the assumptionExpand
Minimizing Uniformly Convex Functions by Cubic Regularization of Newton Method
TLDR
We introduce the notion of second-order condition number of a certain degree and justify the linear rate of convergence in a nondegenerate case for the method with an adaptive estimate of the regularization parameter. Expand
Stochastic Subspace Cubic Newton Method
TLDR
We propose a new randomized second-order optimization algorithm---Stochastic Subspace Cubic Newton (SSCN)---for minimizing a high dimensional convex function $f$. Expand
Convex optimization based on global lower second-order models
TLDR
We present new second-order algorithms for composite convex optimization, called Contracting-domain Newton methods, based on global second- order lower approximation for the smooth component of the objective. Expand
Affine-invariant contracting-point methods for Convex Optimization
TLDR
We present a general framework of Contracting-Point methods, which solve at each iteration an auxiliary subproblem re- stricting the smooth part of the objective function onto contraction of the initial domain. Expand
Optimization Methods for Fully Composite Problems
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimizationExpand
Inexact Tensor Methods with Dynamic Accuracies
TLDR
In this paper, we study inexact high-order Tensor Methods for solving convex optimization problems with composite objective. Expand