Proximal Methods with Bregman Distances to Solve VIP on Hadamard Manifolds with Null Sectional Curvature

Erik Alex Papa Quiroz; Paulo Roberto Oliveira

doi:10.1007/s40305-020-00311-y

Proximal Methods with Bregman Distances to Solve VIP on Hadamard Manifolds with Null Sectional Curvature

Erik Alex Papa Quiroz
, Paulo Roberto Oliveira

Universidad Nacional Mayor de San Marcos
Universidade Federal do Rio de Janeiro

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

Resumen

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.

Idioma original	Inglés
Páginas (desde-hasta)	499-523
Número de páginas	25
Publicación	Journal of the Operations Research Society of China
Volumen	9
N.º	3
DOI	https://doi.org/10.1007/s40305-020-00311-y
Estado	Publicada - set. 2021
Publicado de forma externa	Sí

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title = "Proximal Methods with Bregman Distances to Solve VIP on Hadamard Manifolds with Null Sectional Curvature",

abstract = "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.",

keywords = "Bregman distances, Hadamard manifolds, Monotone vector field, Proximal point methods, Variational inequality problems",

author = "\{Papa Quiroz\}, \{Erik Alex\} and Oliveira, \{Paulo Roberto\}",

note = "Publisher Copyright: {\textcopyright} 2020, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2021",

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doi = "10.1007/s40305-020-00311-y",

language = "English",

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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

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 - https://www.scopus.com/pages/publications/85089312376

U2 - 10.1007/s40305-020-00311-y

DO - 10.1007/s40305-020-00311-y

M3 - Article

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 -

Proximal Methods with Bregman Distances to Solve VIP on Hadamard Manifolds with Null Sectional Curvature

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