Author

Shu-Tai Yang

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Preprint Aug 2026

Optimal Parameter-Free Gradient Minimization in $\ell_p$ Geometry

We study the first-order oracle complexity of finding a queried point with small gradient in $\ell_p$ geometry, with particular attention to the information needed to adapt the unknown smoothness and distance scales. In the strict counted local value--gradient model, no finite complexity bound can depend only on $LR/\e...

Shu-Tai Yang, Yu-Ning Yang · 0 citations

Preprint Aug 2026

The Sharp Worst-Case Asymptotic Rate of the Barzilai--Borwein Method in $\mathbb R^d$ and Hilbert Spaces

We establish sharp asymptotic rates for the two Barzilai--Borwein (BB) rules on uniformly positive quadratics and local nonlinear problems. In finite dimensions, for either fixed rule and an arbitrary positive first step, the gradient root factor is bounded by $(b_0-a_0)/(b_0+a_0)$, where $[a_0,b_0]$ is the initially a...

Shu-Tai Yang, Ya-Xiang Yuan · 1 citation · ⚡1