Iteration-Complexity of Gradient, Subgradient and Proximal Point Methods on Riemannian Manifolds

Glaydston C. Bento (), Orizon P. Ferreira () and Jefferson G. Melo ()
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Glaydston C. Bento: IME, Universidade Federal de Goiás
Orizon P. Ferreira: IME, Universidade Federal de Goiás
Jefferson G. Melo: IME, Universidade Federal de Goiás

Journal of Optimization Theory and Applications, 2017, vol. 173, issue 2, No 9, 548-562

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

Keywords: Complexity; Gradient method; Subgradient method; Proximal point method; Riemannian manifold; 90C30; 49M37; 65K05 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10957-017-1093-4

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