A modified Riemannian hybrid conjugate gradient method for nonconvex optimization problems

This paper proposes a new Riemannian hybrid conjugate gradient method aimed at solving nonconvex optimization problems on Riemannian manifolds. We extend the modified PRP and HS methods (WYL and VHS methods) to Riemannian manifolds, and introduce a new hybrid parameter that ensures the search direction always satisfies the descent property without requiring any line search. The global convergence of the method is established under the Riemannian weak Wolfe conditions. Finally, through numerical comparison with existing Riemannian conjugate gradient methods on five test problems, we validate the effectiveness of the proposed method.