Conjugate Gradient Methods on Riemannian Manifolds

Abstract

In this chapter, we discuss the conjugate gradient (CG) methods on Riemannian manifolds, which we also call Riemannian CG methods. They can be considered to be a modified version of the Riemannian steepest descent method. In particular, we analyze the Fletcher–Reeves-type and Dai–Yuan-type Riemannian CG methods and prove their global convergence properties under some conditions.