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Journal of Convex Analysis 16 (2009), No. 1, 049--069
Copyright Heldermann Verlag 2009

Proximal Point Methods for Quasiconvex and Convex Functions with Bregman Distances on Hadamard Manifolds

Erik A. Papa Quiroz
Universidad Nacional de Callao, Lima, Peru

Paolo Roberto Oliveira
PESC-COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

This paper generalizes the proximal point method using Bregman distances to solve convex and quasiconvex optimization problems on Hadamard manifolds. We will proved that the sequence generated by our method is well defined and converges to an optimal solution of the problem. Also, we obtain the same convergence properties for the classical proximal method, applied to quasiconvex problems. Finally, we give some examples of Bregman distances in non-Euclidean spaces.

Keywords: Proximal point algorithms, Hadamard manifolds, Bregman distances, Bregman functions.

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