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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
On the Complexity of Lower-Order Implementations of Higher-Order Methods
Nikita Doikov, Geovani Nunes Grapiglia
In this work, we propose a method for minimizing non-convex functions with Lipschitz continuous th-order derivatives, starting from . The method, however, only require…
math.OC2025
Gradient-Normalized Smoothness for Optimization with Approximate Hessians
Andrei Semenov, Martin Jaggi, Nikita Doikov
In this work, we develop new optimization algorithms that use approximate second-order information combined with the gradient regularization technique to achieve fast global conver…