The stochastic projected gradient method for optimization problems on Hadamard manifolds
Optimization Eruditorum, Volume 3, Issue 1, April 2026, Pages 20–33
XIAO-BO LI
School of Sciences, Civil Aviation Flight University of China, 618300, People’s Republic of China
YU-KE ZHONG
School of Sciences, Civil Aviation Flight University of China, 618300, People’s Republic of China
Abstract
In this paper, the stochastic projected gradient method for optimization problems is proposed on Hadamard manifolds, which utilize the Riemannian metric and curvature information. Under some specified assumptions on compactness and the problem geometry, the convergence rate of the stochastic projected gradient method for optimization problems is presented. Furthermore, assume in addition that \(f\) is \(\sigma\)-strongly convex for some \(\sigma>0\), some convergence results are also established on Hadamard manifolds.
Cite this Article as
Xiao-Bo Li, Yu-Ke Zhong, The stochastic projected gradient method for optimization problems, Optimization Eruditorum, 3(1), 20–33, 2026