In this paper, we consider the problem of minimizing a continuously differentiable function on the Stiefel manifold. To solve this problem, we develop a geodesic-free proximal point algorithm, which does not require the use of the Riemannian distance. The proposed method can be regarded as an iterative fixed-point method, which repeatedly applies a proximal operator to an initial point. In addition, we establish the global convergence of the new approach without any restrictive assumption. Numerical experiments on linear eigenvalues problems and the minimization of sums of heterogeneous quadratic functions, show that the proposed method is competitive with some procedures existing at the literature.
Report number 1, 05/2021