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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 -enlargement of maximal monotone vector fields is used, and its lower-semicontinuity is established to obtain the method convergence in this new context.
@article{COCV_2020__26_1_A63_0,
author = {Batista, E.E.A. and Bento, G.C. and Ferreira, O.P.},
title = {An extragradient-type algorithm for variational inequality on {Hadamard} manifolds},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {26},
year = {2020},
doi = {10.1051/cocv/2019040},
mrnumber = {4150225},
zbl = {1451.90159},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2019040/}
}
TY - JOUR AU - Batista, E.E.A. AU - Bento, G.C. AU - Ferreira, O.P. TI - An extragradient-type algorithm for variational inequality on Hadamard manifolds JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2019040/ DO - 10.1051/cocv/2019040 LA - en ID - COCV_2020__26_1_A63_0 ER -
%0 Journal Article %A Batista, E.E.A. %A Bento, G.C. %A Ferreira, O.P. %T An extragradient-type algorithm for variational inequality on Hadamard manifolds %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2019040/ %R 10.1051/cocv/2019040 %G en %F COCV_2020__26_1_A63_0
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://geodesic.mathdoc.fr/articles/10.1051/cocv/2019040/
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