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Article

Yin, Lulu ; Liu, Hongwei ; Yang, Jun
Modified golden ratio algorithms for pseudomonotone equilibrium problems and variational inequalities. (English). Applications of Mathematics, vol. 67 (2022), issue 3, pp. 273-296
MSC: 47J25, 49J40, 65K10, 65K15, 90C25, 90C33, 90C48, 91B50 | MR 4409307 | Zbl 07547196 | DOI: 10.21136/AM.2021.0180-20
Keywords:
equilibrium problem; strongly pseudomonotone bifunctions; Lipschitz-type condition; variational inequality; error bound
Summary:
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.
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