An Intrinsic Scaled Riemannian Nonmonotone Conjugate Gradient Method on Stiefel Manifold

In this paper, we focus on the optimization problem on the Stiefel manifold. Based on the inverse process of the QR-type retraction, we propose a new intrinsic vector transport. In combination with Dai’s nonmonotone conjugate gradient (CG) method, we present an intrinsic Riemannian nonmonotone CG method and its scaled version and establish the global convergence of the intrinsic scaled Riemannian nonmonotone CG method. Numerical results on a variety of optimization problems on Stiefel manifolds indicate the effectiveness of the proposed method.