Ya-Xiang Yuan

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...