Modified golden ratio algorithms for pseudomonotone equilibrium problems and variational inequalities

Lulu Yin; Hongwei Liu; Jun Yang

Applications of Mathematics (2022)

  • Volume: 67, Issue: 3, page 273-296
  • ISSN: 0862-7940

Abstract

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We propose a modification of the golden ratio algorithm for solving pseudomonotone equilibrium problems with a Lipschitz-type condition in Hilbert spaces. A new non-monotone stepsize rule is used in the method. Without such an additional condition, the theorem of weak convergence is proved. Furthermore, with strongly pseudomonotone condition, the $R$-linear convergence rate of the method is established. The results obtained are applied to a variational inequality problem, and the convergence rate of the problem under the condition of error bound is considered. Finally, numerical experiments on several specific problems and comparison with other algorithms show the superiority of the algorithm.

How to cite

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Yin, Lulu, Liu, Hongwei, and Yang, Jun. "Modified golden ratio algorithms for pseudomonotone equilibrium problems and variational inequalities." Applications of Mathematics 67.3 (2022): 273-296. <http://eudml.org/doc/298238>.

@article{Yin2022,
abstract = {We propose a modification of the golden ratio algorithm for solving pseudomonotone equilibrium problems with a Lipschitz-type condition in Hilbert spaces. A new non-monotone stepsize rule is used in the method. Without such an additional condition, the theorem of weak convergence is proved. Furthermore, with strongly pseudomonotone condition, the $R$-linear convergence rate of the method is established. The results obtained are applied to a variational inequality problem, and the convergence rate of the problem under the condition of error bound is considered. Finally, numerical experiments on several specific problems and comparison with other algorithms show the superiority of the algorithm.},
author = {Yin, Lulu, Liu, Hongwei, Yang, Jun},
journal = {Applications of Mathematics},
language = {eng},
number = {3},
pages = {273-296},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Modified golden ratio algorithms for pseudomonotone equilibrium problems and variational inequalities},
url = {http://eudml.org/doc/298238},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Yin, Lulu
AU - Liu, Hongwei
AU - Yang, Jun
TI - Modified golden ratio algorithms for pseudomonotone equilibrium problems and variational inequalities
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 3
SP - 273
EP - 296
AB - We propose a modification of the golden ratio algorithm for solving pseudomonotone equilibrium problems with a Lipschitz-type condition in Hilbert spaces. A new non-monotone stepsize rule is used in the method. Without such an additional condition, the theorem of weak convergence is proved. Furthermore, with strongly pseudomonotone condition, the $R$-linear convergence rate of the method is established. The results obtained are applied to a variational inequality problem, and the convergence rate of the problem under the condition of error bound is considered. Finally, numerical experiments on several specific problems and comparison with other algorithms show the superiority of the algorithm.
LA - eng
UR - http://eudml.org/doc/298238
ER -

References

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