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

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 assumption… Expand

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

We propose a new randomized second-order optimization algorithm---Stochastic Subspace Cubic Newton (SSCN)---for minimizing a high dimensional convex function $f$.Expand

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

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

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 minimization… Expand