The Newton Iteration on Lie Groups

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Exponential Barycenters of the Canonical Cartan Connection and Invariant Means on Lie Groups (2013, unknown): “Notable exceptions are [51, 47] which propose Newton algorithms to optimize general functions on non compact Lie groups based on Cartan-Schouten connections.”
Lie-group methods (2000, background): “Recently, however, Owren and Welfert (1996) developed two variants of Newton’s method that always evolve in G.”
Lie group methods (2009, unknown): “Recently, however, Owren and Welfert (1996) developed two variants of Newton’s method that always evolve in G.”
A feasible method for optimization with orthogonality constraints (2012, methodology): “Newton’s methods, such as those in [2, 18, 40, 49, 50, 52], use the second-order information of the objective function to achieve super-linear convergence.”
Newton's method on Riemannian manifolds and a geometric model for the human spine (2002, methodology): “…used retractions as we do here; Udriste (1994) studied Newton’s method to find the zeros of a gradient vector field defined on a Riemannian manifold; Owren & Welfert (1996) defined Newton iteration for solving the equation F(x) = 0 where F is a map from a Lie group to its corresponding Lie…”