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Title of Journal: J Optim Theory Appl

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Abbravation: Journal of Optimization Theory and Applications

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Springer US

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1573-2878

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A New Approach to the Proximal Point Method Conve

Authors: Glaydston de Carvalho Bento João Xavier da Cruz Neto Paulo Roberto Oliveira
Publish Date: 2016/01/11
Volume: 168, Issue: 3, Pages: 743-755
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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 constantG C Bento was supported in part by CAPESMESCUBA 226/2012 FAPEG 20121026700090905/2012 and CNPq Grants 458479/20144 471815/20128 303732/20113 312077/ 20149 J X Cruz Neto was partially supported by CNPq GRANT 305462/20148 and P R Oliveira was supported in part by CNPq

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