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

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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.

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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

  1. Universidade Federal do Oeste da Bahia, Barreiras, BA, 47808-021, Brazil

    Edvaldo E. A. Batista

  2. IME, Universidade Federal de Goiás, Goiânia, GO, 74001-970, Brazil

    Glaydston de Carvalho Bento & Orizon P. Ferreira

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  1. Edvaldo E. A. Batista
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  2. Glaydston de Carvalho Bento
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  3. Orizon P. Ferreira
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Correspondence to Edvaldo E. A. Batista.

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Batista, E.E.A., Bento, G.C. & Ferreira, O.P. Enlargement of Monotone Vector Fields and an Inexact Proximal Point Method for Variational Inequalities in Hadamard Manifolds. J Optim Theory Appl 170, 916–931 (2016). https://doi.org/10.1007/s10957-016-0982-2

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  • DOI: https://doi.org/10.1007/s10957-016-0982-2

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