An extragradient-type algorithm for variational inequality on Hadamard manifolds
ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 63.

This paper presents an extragradient method for variational inequality associated with a point-to-set vector field in Hadamard manifolds, and a study of its convergence properties. To present our method, the concept of ϵ -enlargement of maximal monotone vector fields is used, and its lower-semicontinuity is established to obtain the method convergence in this new context.

DOI : 10.1051/cocv/2019040
Classification : 90C33, 65K05, 47J25
Mots-clés : Extragradient algorithm, Hadamard manifolds, $\epsilon$-enlargement, lower semicontinuity 
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     title = {An extragradient-type algorithm for variational inequality on {Hadamard} manifolds},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
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Batista, E.E.A.; Bento, G.C.; Ferreira, O.P. An extragradient-type algorithm for variational inequality on Hadamard manifolds. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 63. doi : 10.1051/cocv/2019040. http://archive.numdam.org/articles/10.1051/cocv/2019040/

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