TY - JOUR
T1 - Proximal Methods with Bregman Distances to Solve VIP on Hadamard Manifolds with Null Sectional Curvature
AU - Papa Quiroz, Erik Alex
AU - Oliveira, Paulo Roberto
N1 - Publisher Copyright:
© 2020, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2021/9
Y1 - 2021/9
N2 - We present an extension of the proximal point method with Bregman distances to solve variational inequality problems (VIP) on Hadamard manifolds with null sectional curvature. Under some natural assumptions, as for example, the existence of solutions of the VIP and the monotonicity of the multivalued vector field, we prove that the sequence of the iterates given by the method converges to a solution of the problem. Furthermore, this convergence is linear or superlinear with respect to the Bregman distance.
AB - We present an extension of the proximal point method with Bregman distances to solve variational inequality problems (VIP) on Hadamard manifolds with null sectional curvature. Under some natural assumptions, as for example, the existence of solutions of the VIP and the monotonicity of the multivalued vector field, we prove that the sequence of the iterates given by the method converges to a solution of the problem. Furthermore, this convergence is linear or superlinear with respect to the Bregman distance.
KW - Bregman distances
KW - Hadamard manifolds
KW - Monotone vector field
KW - Proximal point methods
KW - Variational inequality problems
UR - http://www.scopus.com/inward/record.url?scp=85089312376&partnerID=8YFLogxK
U2 - 10.1007/s40305-020-00311-y
DO - 10.1007/s40305-020-00311-y
M3 - Artículo
AN - SCOPUS:85089312376
SN - 2194-668X
VL - 9
SP - 499
EP - 523
JO - Journal of the Operations Research Society of China
JF - Journal of the Operations Research Society of China
IS - 3
ER -