Two efficient Riemannian Dai-Liao type conjugate gradient methods for solving smooth objective functions on Riemannian manifold

In this paper, we develop an efficient Riemannian Dai-Liao type conjugate gradient methods for minimizing smooth objective functions on Riemannian manifold. This method is based on a Riemannian generalization of the Dai-Liao conjugate gradient method in Euclidean space. We establish the sufficient descent condition of the proposed algorithm and prove its global convergence under two assumptions. Moreover, we present an alternative variant of this method. Finally, we conduct numerical comparisons between the newly developed methods and existing approaches by solving the graphs on the unit sphere. Performance profiles confirm the efficacy and superior performance of the proposed methods over existing approaches, and demonstrate its broad applicability across diverse graph structures.