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arXiv · 1609.04869

Iteration-complexity of gradient, subgradient and proximal point methods on Riemannian manifolds

G. C. Bento·O. P. Ferreira·J. G. Melo
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Abstract

This paper considers optimization problems on Riemannian manifolds and analyzes iteration-complexity for gradient and subgradient methods on manifolds with non-negative curvature. By using tools from the Riemannian convex analysis and exploring directly the tangent space of the manifold, we obtain different iteration-complexity bounds for the aforementioned methods, complementing and improving related results. Moreover, we also establish iteration-complexity bound for the proximal point method on Hadamard manifolds.

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G. C. Bento, O. P. Ferreira, J. G. Melo. 2016-09-15. Iteration-complexity of gradient, subgradient and proximal point methods on Riemannian manifolds. https://arxiv.org/abs/1609.04869

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