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

  • Glaydston C. Bento
  • Orizon P. Ferreira
  • Jefferson G. MeloEmail author


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.


Complexity Gradient method Subgradient method Proximal point method Riemannian manifold 

Mathematics Subject Classification

90C30 49M37 65K05 



This work was supported by CNPq Grants 458479/2014-4, 312077/2014-9, 305158/2014-7, 444134/2014-0, 406975/2016-7.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.IME, Universidade Federal de GoiásGoiâniaBrazil

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