Geodesic
Modified golden ratio algorithms for pseudomonotone equilibrium problems and variational inequalities
Applications of Mathematics, Tome 67 (2022) no. 3, pp. 273-296

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.21136/AM.2021.0180-20
Classification : 47J25, 49J40, 65K10, 65K15, 90C25, 90C33, 90C48, 91B50
Keywords: equilibrium problem; strongly pseudomonotone bifunctions; Lipschitz-type condition; variational inequality; error bound 
@article{10_21136_AM_2021_0180_20,
     author = {Yin, Lulu and Liu, Hongwei and Yang, Jun},
     title = {Modified golden ratio algorithms for pseudomonotone equilibrium problems and variational inequalities},
     journal = {Applications of Mathematics},
     pages = {273--296},
     publisher = {mathdoc},
     volume = {67},
     number = {3},
     year = {2022},
     doi = {10.21136/AM.2021.0180-20},
     mrnumber = {4409307},
     zbl = {07547196},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2021.0180-20/}
}
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
SP  - 273
EP  - 296
VL  - 67
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.2021.0180-20/
DO  - 10.21136/AM.2021.0180-20
LA  - en
ID  - 10_21136_AM_2021_0180_20
ER  - 
%0 Journal Article
%A Yin, Lulu
%A Liu, Hongwei
%A Yang, Jun
%T Modified golden ratio algorithms for pseudomonotone equilibrium problems and variational inequalities
%J Applications of Mathematics
%D 2022
%P 273-296
%V 67
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.2021.0180-20/
%R 10.21136/AM.2021.0180-20
%G en
%F 10_21136_AM_2021_0180_20
Yin, Lulu; Liu, Hongwei; Yang, Jun. Modified golden ratio algorithms for pseudomonotone equilibrium problems and variational inequalities. Applications of Mathematics, Tome 67 (2022) no. 3, pp. 273-296. doi: 10.21136/AM.2021.0180-20

Cité par Sources :