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math.OC2023
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…
math.OC2023
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…