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10 papers · 2 filters
Contracting Proximal Methods for Smooth Convex Optimization
Nikita Doikov, Yurii Nesterov
In this paper, we propose new accelerated methods for smooth convex optimization, called contracting proximal methods. At every step of these methods, we need to minimize a contrac…
Local convergence of tensor methods
Nikita Doikov, Yurii Nesterov
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 u…
On Inexact Solution of Auxiliary Problems in Tensor Methods for Convex Optimization
Geovani Nunes Grapiglia, Yurii Nesterov
In this paper we study the auxiliary problems that appear in -order tensor methods for unconstrained minimization of convex functions with -Hölder continuous th derivative…
Smoothness parameter of power of Euclidean norm
Anton Rodomanov, Yurii Nesterov
In this paper, we study derivatives of powers of Euclidean norm. We prove their Hölder continuity and establish explicit expressions for the corresponding constants. We show that t…
Tensor Methods for Finding Approximate Stationary Points of Convex Functions
Geovani Nunes Grapiglia, Yurii Nesterov
In this paper we consider the problem of finding -approximate stationary points of convex functions that are -times differentiable with -Hölder continuous th derivative…
An entropy-based bound for the computational complexity of a switched system
Benoît Legat, Pablo A. Parrilo, Raphaël M. Jungers
The joint spectral radius (JSR) of a set of matrices characterizes the maximal asymptotic growth rate of an infinite product of matrices of the set. This quantity appears in a numb…