Journal of Optimization Theory and Applications

, Volume 170, Issue 3, pp 916–931

# 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
Article

## Abstract

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.

## Keywords

Enlargement of vector fields Inexact proximal Constrained optimization Hadamard manifold

## Mathematics Subject Classification

90C33 65K05 47J25

## Notes

### Acknowledgments

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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## 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