4 papers
The Sharp Worst-Case Asymptotic Rate of the Barzilai--Borwein Method in and Hilbert Spaces
Shutai Yang, Ya-Xiang Yuan
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 r…
Optimization on product manifolds under a preconditioned metric
Bin Gao, Renfeng Peng, Ya-xiang Yuan
Since optimization on Riemannian manifolds relies on the chosen metric, it is appealing to know that how the performance of a Riemannian optimization method varies with different m…
Symplectic Discretization Approach for Developing New Proximal Point Algorithm
Ya-xiang Yuan, Yi Zhang
The rapid advancements in high-dimensional statistics and machine learning have increased the use of first-order methods. Many of these methods can be regarded as instances of the…
Linear convergence of forward-backward accelerated algorithms without knowledge of the modulus of strong convexity
Bowen Li, Bin Shi, Ya-xiang Yuan
A significant milestone in modern gradient-based optimization was achieved with the development of Nesterov's accelerated gradient descent (NAG) method. This forward-backward techn…