Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

João Xavier Cruz Neto

Dept. of Mathematics, Federal University of Piauí, Teresina, Brazil

jxavier@ufpi.edu.br

I. D. Melo

Dept. of Mathematics, Federal University of Piauí, Teresina, Brazil

P.A. Sousa

Dept. of Mathematics, Federal University of Piauí, Teresina, Brazil

L. P. Silva

Dept. of Mathematics, Federal University of Piauí, Teresina, Brazil

Keywords

  • Proximal point algorithm
  • Hadamard manifold
  • convex funtion
  • quasiconvex function
  • Bregman distance
  • sectional curvature

Mathematics Subject Classification

65K05, 47J25,90C33,91E10

Suggested citation

J. X. Cruz Neto, I. D. Melo, P.A. Sousa, L. 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 24 (2017), No. 2, 679–684. https://doi.org/10.68381/jca24042

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Published by Heldermann Verlag, 2017. Rights now held by Banach Press.