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Subgradient Projection Algorithms for Convex Feasibility on Riemannian Manifolds with Lower Bounded Curvatures

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Abstract

Under the assumption that the sectional curvature of the manifold is bounded from below, we establish convergence result about the cyclic subgradient projection algorithm for convex feasibility problem presented in a paper by Bento and Melo on Riemannian manifolds (J Optim Theory Appl 152, 773–785, 2012). If, additionally, we assume that a Slater type condition is satisfied, then we further show that, without changing the step size, this algorithm terminates in a finite number of iterations. Clearly, our results extend the corresponding ones due to Bento and Melo and, in particular, we solve partially the open problem proposed in the paper by Bento and Melo.

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Acknowledgments

Research of the second author is supported in part by the National Natural Science Foundation of China (Grants 11171300, 11371325) and by Zhejiang Provincial Natural Science Foundation of China (Grant LY13A010011). Research of the third author was partially supported by the National Science Council of Taiwan under Grant NSC 99-2115-M-037-002-MY3.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, People’s Republic of China

    X. M. Wang & C. Li

  2. College of Science, Guizhou University, Guiyang, 550025, People’s Republic of China

    X. M. Wang

  3. Center for General Education, Kaohsiung Medical University, Kaohsiung, 80702, Taiwan

    J. C. Yao

  4. Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    J. C. Yao

Authors
  1. X. M. Wang
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  2. C. Li
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  3. J. C. Yao
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Correspondence to J. C. Yao.

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Communicated by Sándor Zoltán Németh.

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Wang, X.M., Li, C. & Yao, J.C. Subgradient Projection Algorithms for Convex Feasibility on Riemannian Manifolds with Lower Bounded Curvatures. J Optim Theory Appl 164, 202–217 (2015). https://doi.org/10.1007/s10957-014-0568-9

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  • DOI: https://doi.org/10.1007/s10957-014-0568-9

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