Adaptive Trust-Region Method on Riemannian Manifold

We propose an adaptive trust-region method for Riemannian optimization problems. Especially, the trust-region radius converges to zero with the adaptive technique, and the trust-region subproblem is solved by the truncated three-term conjugate gradient method with new restart strategies. We present some properties of this Riemannian method and establish the global convergence and local superlinear convergence under some mild assumptions. Numerical results for the Rayleigh quotient minimization problem, Principal Component Analysis problem, and joint diagonalization problem are reported to demonstrate the effectiveness of the proposed Riemannian method.