Journal of Optimization Theory and Applications

, Volume 170, Issue 3, pp 916–931 | Cite as

Enlargement of Monotone Vector Fields and an Inexact Proximal Point Method for Variational Inequalities in Hadamard Manifolds

  • Edvaldo E. A. Batista
  • Glaydston de Carvalho Bento
  • Orizon P. Ferreira


In this paper, an inexact proximal point method for variational inequalities in Hadamard manifolds is introduced and its convergence properties are studied. To present our method, we generalize the concept of enlargement of monotone operators, from a linear setting to the Riemannian context. As an application, an inexact proximal point method for constrained optimization problems is obtained.


Enlargement of vector fields Inexact proximal Constrained optimization Hadamard manifold 

Mathematics Subject Classification

90C33 65K05 47J25 



The work was supported by FAPEG and CNPq Grants 458479/2014-4, 471815/2012-8, 303732/2011-3, 312077/2014-9, 305158/2014-7.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Edvaldo E. A. Batista
    • 1
  • Glaydston de Carvalho Bento
    • 2
  • Orizon P. Ferreira
    • 2
  1. 1.Universidade Federal do Oeste da BahiaBarreirasBrazil
  2. 2.IMEUniversidade Federal de GoiásGoiâniaBrazil

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