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math.OC2026
On the Complexity of Finding Stationary Points of p-th Order Hölder Smooth Functions in One Dimension
Huanjian Zhou, Taiji Suzuki
We study the query complexity of finding an an -stationary points of a one-dimensional non-convex function whose -th derivative is -Hölder continuous. We deter…
math.OC2026
Finding Stationary Points under Higher-Order Smoothness: Trapping Algorithms and First-Order Lower Bounds
Huanjian Zhou, Masashi Sugiyama, Taiji Suzuki
We study the query complexity of finding approximate stationary points under higher-order smoothness using only function values or only gradients. Our results cover different dimen…
math.OC2025
The Adaptive Complexity of Finding a Stationary Point
Huanjian Zhou, Andi Han, Akiko Takeda +1
In large-scale applications, such as machine learning, it is desirable to design non-convex optimization algorithms with a high degree of parallelization. In this work, we study th…