Journal
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
Volume 173, Issue 2, Pages 548-562Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10957-017-1093-4
Keywords
Complexity; Gradient method; Subgradient method; Proximal point method; Riemannian manifold
Funding
- CNPq [458479/2014-4, 312077/2014-9, 305158/2014-7, 444134/2014-0, 406975/2016-7]
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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.
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