A New Approach to the Proximal Point Method: Convergence on General Riemannian Manifolds

Glaydston Carvalho Bento (), João Xavier Cruz Neto () and Paulo Roberto Oliveira ()
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Glaydston Carvalho Bento: Universidade Federal de Goiás
João Xavier Cruz Neto: Universidade Federal do Piauí
Paulo Roberto Oliveira: Universidade Federal do Rio de Janeiro

Journal of Optimization Theory and Applications, 2016, vol. 168, issue 3, No 1, 743-755

Abstract: Abstract In this paper, we present a new approach to the proximal point method in the Riemannian context. In particular, without requiring any restrictive assumptions about the sign of the sectional curvature of the manifold, we obtain full convergence for any bounded sequence generated by the proximal point method, in the case that the objective function satisfies the Kurdyka–Lojasiewicz inequality. In our approach, we extend the applicability of the proximal point method to be able to solve any problem that can be formulated as the minimizing of a definable function, such as one that is analytic, restricted to a compact manifold, on which the sign of the sectional curvature is not necessarily constant.

Keywords: Proximal method; Non-convex optimization; Kurdyka–Lojasiewicz inequality; Riemannian manifolds; 49J52; 65K05; 58C99; 90C26; 90C56 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10957-015-0861-2

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