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 () and Orizon P. Ferreira ()
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Edvaldo E. A. Batista: Universidade Federal do Oeste da Bahia
Glaydston de Carvalho Bento: Universidade Federal de Goiás
Orizon P. Ferreira: Universidade Federal de Goiás

Journal of Optimization Theory and Applications, 2016, vol. 170, issue 3, No 12, 916-931

Abstract: 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; 90C33; 65K05; 47J25 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-016-0982-2

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