This chapter provides a detailed development of the archetypal second-order optimization method, Newton’s method, as an iteration on manifolds. We propose a formulation of Newton’s method for computing the zeros of a vector field on a manifold equipped with an affine connection and a retraction. In particular, when the manifold is Riemannian, this geometric Newton method can be used to compute critical points of a cost function by seeking the zeros of its gradient vector field. In the case where the underlying space is Euclidean, the proposed algorithm reduces to the classical Newton method. Although the algorithm formulation is provided

EP - 135 PB - Princeton University Press PY - 2008 SN - 9780691132983 SP - 111 T2 - Optimization Algorithms on Matrix Manifolds UR - http://www.jstor.org/stable/j.ctt7smmk.11 Y2 - 2021/09/28/ ER -