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Subgradient Method for Convex Feasibility on Riemannian Manifolds

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Abstract

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.

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  1. IME-Universidade Federal de Goiás, Goiânia, GO, 74001-970, Brazil

    Glaydston C. Bento & Jefferson G. Melo

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  1. Glaydston C. Bento
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  2. Jefferson G. Melo
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Correspondence to Jefferson G. Melo.

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Bento, G.C., Melo, J.G. Subgradient Method for Convex Feasibility on Riemannian Manifolds. J Optim Theory Appl 152, 773–785 (2012). https://doi.org/10.1007/s10957-011-9921-4

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  • DOI: https://doi.org/10.1007/s10957-011-9921-4

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