Proximal point methods for quasiconvex and convex functions with Bregman distances on Hadamard manifolds

E. A.Papa Quiroz, P. Roberto Oliveira

Research output: Contribution to journalArticle

58 Scopus citations

Abstract

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. © Heldermann Verlag.
Original languageAmerican English
Pages (from-to)49-69
Number of pages21
JournalJournal of Convex Analysis
StatePublished - 5 Aug 2009
Externally publishedYes

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