Subgradient Method for Convex Feasibility on Riemannian Manifolds

Glaydston C. Bento () and Jefferson G. Melo ()
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Glaydston C. Bento: IME-Universidade Federal de Goiás
Jefferson G. Melo: IME-Universidade Federal de Goiás

Journal of Optimization Theory and Applications, 2012, vol. 152, issue 3, No 12, 773-785

Abstract: 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.

Keywords: Nonsmooth analysis; Feasibility problem; General convexity; Subgradient algorithm; Riemannian manifolds (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (15)

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DOI: 10.1007/s10957-011-9921-4

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