20 citations · 51 across the 8 of their papers we have counts for
13 papers
Smooth Monotone Stochastic Variational Inequalities and Saddle Point Problems: A Survey
Aleksandr Beznosikov, Boris Polyak, Eduard Gorbunov +2
This paper is a survey of methods for solving smooth (strongly) monotone stochastic variational inequalities. To begin with, we give the deterministic foundation from which the sto…
Stopping Rules for Gradient Methods for Non-Convex Problems with Additive Noise in Gradient
Boris T. Polyak, Ilia A. Kuruzov, Fedor S. Stonyakin
We study the gradient method under the assumption that an additively inexact gradient is available for, generally speaking, non-convex problems. The non-convexity of the objective…
Optimizing Static Linear Feedback: Gradient Method
Ilyas Fatkhullin, Boris Polyak
The linear quadratic regulator is the fundamental problem of optimal control. Its state feedback version was set and solved in the early 1960s. However the static output feedback p…
Sparse solutions of optimal control via Newton method for under-determined systems
Boris Polyak, Andrey Tremba
We focus on finding sparse and least--norm solutions for unconstrained nonlinear optimal control problems. Such optimization problems are non-convex and non-smooth, neverth…
Gradient projection and conditional gradient methods for constrained nonconvex minimization
Maxim Balashov, Boris Polyak, Andrey Tremba
Minimization of a smooth function on a sphere or, more generally, on a smooth manifold, is the simplest non-convex optimization problem. It has a lot of applications. Our goal is t…
Non-monotone Behavior of the Heavy Ball Method
Marina Danilova, Anastasiya Kulakova, Boris Polyak
We focus on the solutions of second-order stable linear difference equations and demonstrate that their behavior can be non-monotone and exhibit peak effects depending on initial c…