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math.OC2025
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…
math.OC2025
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…