In this paper we deal with non-monotone line-search methods to minimize a smooth cost function on a Riemannian
manifold. In particular, we study the number of iterations necessary for this class of algorithms to obtain
e-approximated stationary points. Specifically, we prove that under a regularity Lipschitz-type condition
on the pullbacks of the cost function to the tangent spaces of the manifold and other mild assumptions, the
Riemannian non-monotone line-search methods generates points with Riemannian gradient norm smaller than
e in O(1/(e^2)) iterations. Our worst-case complexity includes a wide variety of known
non-monotone strategies existing in the literature. Additionally, we establish the global convergence for this
family of methods. The bounds obtained in our analysis agree with the bounds known for line-search methods in the
field of unconstrained nonlinear optimization and hence generalizes previous work.
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