Geodesic
A Note on the Paper "Proximal Point Methods for Quasiconvex and Convex Functions with Bregman Distances on Hadamard Manifolds"
Journal of convex analysis, Tome 24 (2017) no. 2, pp. 679-684
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We provide an erratum to Proposition 3.4 of E. A. Papa Quiroz and P. R. Oliveira in their article "Proximal point methods for quasiconvex and convex functions with Bregman distances on Hadamard manifolds" [J. Convex Analysis 16(1) (2009) 49--69]. More specifically, we prove that the function associated with the exponential map in this proposition is not convex on Hadamard manifolds with negative sectional curvature, and present an alternative proof for the result in the case of null sectional curvature.
Classification : 65K05, 47J25,90C33,91E10
Mots-clés : Proximal point algorithm, Hadamard manifold, convex funtion, quasiconvex function, Bregman distance, sectional curvature 
@article{JCA_2017_24_2_JCA_2017_24_2_a18,
     author = {J. X. Cruz Neto and I. D. Melo and P.A. Sousa and J. P. Silva},
     title = {A {Note} on the {Paper} {"Proximal} {Point} {Methods} for {Quasiconvex} and {Convex} {Functions} with {Bregman} {Distances} on {Hadamard} {Manifolds"}},
     journal = {Journal of convex analysis},
     pages = {679--684},
     year = {2017},
     volume = {24},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_2_JCA_2017_24_2_a18/}
}
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J. X. Cruz Neto; I. D. Melo; P.A. Sousa; J. P. Silva. A Note on the Paper "Proximal Point Methods for Quasiconvex and Convex Functions with Bregman Distances on Hadamard Manifolds". Journal of convex analysis, Tome 24 (2017) no. 2, pp. 679-684. http://geodesic.mathdoc.fr/item/JCA_2017_24_2_JCA_2017_24_2_a18/