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About the Convexity of a Special Function on Hadamard Manifolds.

J. X. Cruz Neto (jxavier***at***ufpi.edu.br)
I.D. Melo (italodowell***at***ufpi.edu.br)
P.A. Sousa (paulosousa***at***ufpi.edu.br)
J.P. Silva (jsilva***at***ufpi.edu.br)

Abstract: In this article we provide an erratum to Proposition 3.4 of E.A. Papa Quiroz and P.R. Oliveira. Proximal Point Methods for Quasiconvex and Convex Functions with Bregman Distances on Hadamard Manifolds, Journal of Convex Analysis 16 (2009), 49-69. More specifically, we prove that the function defined by the product of a fixed vector in the space tangent by inverse of the exponential application at a given pointis 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.

Keywords: Proximal algorithms; Convex Functions; Hadamard Manifolds

Category 1: Convex and Nonsmooth Optimization (Generalized Convexity/Monoticity )

Citation: Federal University of PiauĂ­ - Brazil, march/2014

Download: [PDF]

Entry Submitted: 03/22/2014
Entry Accepted: 03/22/2014
Entry Last Modified: 03/28/2014

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