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

X. M. Wang (), C. Li () and J. C. Yao ()
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X. M. Wang: Zhejiang University
C. Li: Zhejiang University
J. C. Yao: Kaohsiung Medical University

Journal of Optimization Theory and Applications, 2015, vol. 164, issue 1, No 10, 202-217

Abstract: 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.

Keywords: Convex feasibility problem; Cyclic subgradient projection algorithm; Riemannian manifold; Sectional curvature; 90C25; 68U05; 65K05 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10957-014-0568-9

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