4 papers
Improved global performance guarantees of second-order methods in convex minimization
Pavel Dvurechensky, Yurii Nesterov
In this paper, we attempt to compare two distinct branches of research on second-order optimization methods. The first one studies self-concordant functions and barriers, the main…
An optimal lower bound for smooth convex functions
Mihai I. Florea, Yurii Nesterov
First order methods endowed with global convergence guarantees operate using global lower bounds on the objective. The tightening of the bounds has been shown to increase both the…
Super-Universal Regularized Newton Method
Nikita Doikov, Konstantin Mishchenko, Yurii Nesterov
We analyze the performance of a variant of Newton method with quadratic regularization for solving composite convex minimization problems. At each step of our method, we choose reg…
Gradient Regularization of Newton Method with Bregman Distances
Nikita Doikov, Yurii Nesterov
In this paper, we propose a first second-order scheme based on arbitrary non-Euclidean norms, incorporated by Bregman distances. They are introduced directly in the Newton iterate…