An adaptive Riemannian spectral gradient method without cost function evaluations

This work addresses a spectral correction for the adaptive weighted normalized gradient method in the minimization of smooth functions on a Riemannian manifold. The proposed algorithm incorporates a Barzilai-Borwein-type stepsize in order to accelerate the Riemannian gradient procedure. The new approach is globally convergent and does not require evaluating the objective function throughout the iterative process. Our preliminary numerical experiments show that the use of spectral correction improves the performance of the adaptive Riemannian gradient method.