Annals of Mathematical Sciences and Applications

In this note we refine some of the results of [$\href{https://mathscinet.ams.org/mathscinet/relay-station?mr=2818926}{18}$] on the gradient-projection algorithm in the infinite-dimensional Hilbert space setting by weakening the conditions imposed on the choices of the parameters in [$\href{https://mathscinet.ams.org/mathscinet/relay-station?mr=2818926}{18}$, Theorems 4.2, 4.3 and 5.2]. In addition, we also show that the relaxed gradient-projection algorithm has a sublinear rate of convergence.