Global convergence of Hager–Zhang type Riemannian conjugate gradient method

This paper presents the Hager–Zhang (HZ)-type Riemannian conjugate gradient method that uses exponential retraction. We also present global convergence analyses of our proposed under two kinds assumptions. Moreover, we numerically compare methods with existing by solving optimization problems on unit sphere. The numerical results show has much better performance than methods, i.e., FR, DY, PRP, and HS methods. In particular, they it higher including hybrid ones in computing stability number graphs problem.