New retraction-based backtracking gradient and Newton-type algorithms on Riemannian manifolds and Banach spaces are claimed to converge to local minima and to avoid saddle points for random starting points.
Armijo, Minimization of functions having Lipschitz continuous first partial derivatives, Pacific J
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Some iterative algorithms on Riemannian manifolds and Banach spaces with good global convergence guarantee
New retraction-based backtracking gradient and Newton-type algorithms on Riemannian manifolds and Banach spaces are claimed to converge to local minima and to avoid saddle points for random starting points.