1 citations · 1 across the 5 of their papers we have counts for
5 papers
Universal Reduced-Operator Method and High-Order Global Curvature Bounds
Nikita Doikov, Yurii Nesterov
In this paper, we develop a new concept of Global Curvature Bound (GCB) for an arbitrary nonlinear operator between abstract metric spaces. We use this notion to characterize the g…
Universal Complexity Bounds for Universal Gradient Methods in Nonlinear Optimization
Yurii Nesterov
In this paper, we provide the universal first-order methods of Composite Optimization with new complexity analysis. It delivers some universal convergence guarantees, which are not…
Local and Global Convergence of Greedy Parabolic Target-Following Methods for Linear Programming
Yurii Nesterov
In the first part of this paper, we prove that, under some natural non-degeneracy assumptions, the Greedy Parabolic Target-Following Method, based on {\em universal tangent directi…
High-Order Reduced-Gradient Methods for Composite Variational Inequalities
Yurii Nesterov
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced G…
Quartic Regularity
Yurii Nesterov
In this paper, we propose new linearly convergent second-order methods for minimizing convex quartic polynomials. This framework is applied for designing optimization schemes, whic…