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.