An inexact Riemannian proximal gradient method

This paper considers the problem of minimizing summation a differentiable function and nonsmooth on Riemannian manifold. In recent years, proximal gradient method its variants have been generalized to setting for solving such problems. Different approaches generalize mapping lead different versions methods. However, their convergence analyses all rely exactly, which is either too expensive or impracticable. this paper, we study an inexact method. It proven that if solved sufficiently accurately, then global local rate based Kurdyka–Łojasiewicz property can be guaranteed. Moreover, practical conditions accuracy are provided. As byproduct, Stiefel manifold proposed in Chen et al. [SIAM J Optim 30(1):210–239, 2020] viewed as provided certain accuracy. Finally, numerical experiments sparse principal component analysis conducted test conditions.