Subgradient Algorithm on Riemannian Manifolds

O. P. Ferreira and P. R. Oliveira
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O. P. Ferreira: Universidade Federal de Goiás
P. R. Oliveira: Universidade Federal do Rio de Janeiro

Journal of Optimization Theory and Applications, 1998, vol. 97, issue 1, No 6, 93-104

Abstract: Abstract The subgradient method is generalized to the context of Riemannian manifolds. The motivation can be seen in non-Euclidean metrics that occur in interior-point methods. In that frame, the natural curves for local steps are the geodesies relative to the specific Riemannian manifold. In this paper, the influence of the sectional curvature of the manifold on the convergence of the method is discussed, as well as the proof of convergence if the sectional curvature is nonnegative.

Keywords: Nondifferentiable optimization; convex programming; subgradient methods; Riemannian manifolds (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (19)

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DOI: 10.1023/A:1022675100677

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