500 citations · 1.2k across the 44 of their papers we have counts for
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Convex quartic problems: homogenized gradient method and preconditioning
Radu-Alexandru Dragomir, Yurii Nesterov
We consider a convex minimization problem for which the objective is the sum of a homogeneous polynomial of degree four and a linear term. Such task arises as a subproblem in algor…
Gradient Methods for Stochastic Optimization in Relative Scale
Yurii Nesterov, Anton Rodomanov
We propose a new concept of a relatively inexact stochastic subgradient and present novel first-order methods that can use such objects to approximately solve convex optimization p…
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…
Adaptive Third-Order Methods for Composite Convex Optimization
Geovani Nunes Grapiglia, Yurii Nesterov
In this paper we propose third-order methods for composite convex optimization problems in which the smooth part is a three-times continuously differentiable function with Lipschit…
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…
High-order methods beyond the classical complexity bounds, II: inexact high-order proximal-point methods with segment search
Masoud Ahookhosh, Yurii Nesterov
A bi-level optimization framework (BiOPT) was proposed in [3] for convex composite optimization, which is a generalization of bi-level unconstrained minimization framework (BLUM) g…