A Riemannian subspace limited-memory SR1 trust region method

In this paper, we present a new trust region algorithm on any compact Riemannian manifolds using subspace techniques. The global convergence of the method is proved and local \(d+1\)-step superlinear convergence of the algorithm is presented, where d is the dimension of the Riemannian manifold. Our numerical results show that the proposed subspace algorithm is competitive to some recent developed methods, such as the LRTR-SR1 method, the LRTR-BFGS method, the Riemannian CG method.