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

Carvalho Bento, Glaydston ; Cruz Neto, João ; Oliveira, Paulo

Journal of Optimization Theory and Applications, 2016, Vol.168(3), pp.743-755 [Periódico revisado por pares]

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  • Título:
    A New Approach to the Proximal Point Method: Convergence on General Riemannian Manifolds
  • Autor: Carvalho Bento, Glaydston ; Cruz Neto, João ; Oliveira, Paulo
  • Assuntos: Proximal method ; Non-convex optimization ; Kurdyka–Lojasiewicz inequality ; Riemannian manifolds
  • É parte de: Journal of Optimization Theory and Applications, 2016, Vol.168(3), pp.743-755
  • Descrição: 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.
  • Idioma: Inglês

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