Geodesic
Proximal Point Methods for Quasiconvex and Convex Functions with Bregman Distances on Hadamard Manifolds
Journal of convex analysis, Tome 16 (2009) no. 1, pp. 49-69 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Mots-clés : Proximal point algorithms, Hadamard manifolds, Bregman distances, Bregman functions 
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     author = {E. A. Papa Quiroz and P. R. Oliveira},
     title = {Proximal {Point} {Methods} for {Quasiconvex} and {Convex} {Functions} with {Bregman} {Distances} on {Hadamard} {Manifolds}},
     journal = {Journal of convex analysis},
     pages = {49--69},
     year = {2009},
     volume = {16},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2009_16_1_JCA_2009_16_1_a2/}
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E. A. Papa Quiroz; P. R. Oliveira. Proximal Point Methods for Quasiconvex and Convex Functions with Bregman Distances on Hadamard Manifolds. Journal of convex analysis, Tome 16 (2009) no. 1, pp. 49-69. http://geodesic.mathdoc.fr/item/JCA_2009_16_1_JCA_2009_16_1_a2/