Subgradient Method for Convex Feasibility on Riemannian Manifolds

  • Glaydston C. Bento
  • Jefferson G. Melo


In this paper, a subgradient type algorithm for solving convex feasibility problem on Riemannian manifold is proposed and analysed. The sequence generated by the algorithm converges to a solution of the problem, provided the sectional curvature of the manifold is non-negative. Moreover, assuming a Slater type qualification condition, we analyse a variant of the first algorithm, which generates a sequence with finite convergence property, i.e., a feasible point is obtained after a finite number of iterations. Some examples motivating the application of the algorithm for feasibility problems, nonconvex in the usual sense, are considered.


Nonsmooth analysis Feasibility problem General convexity Subgradient algorithm Riemannian manifolds 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.IME-Universidade Federal de GoiásGoiâniaBrazil

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