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The extragradient algorithm with inertial effects extended to equilibrium problems.
- Source :
- Computational & Applied Mathematics; May2020, Vol. 39 Issue 2, p1-26, 26p
- Publication Year :
- 2020
-
Abstract
- In this paper, two algorithms are proposed for a class of pseudomonotone and strongly pseudomonotone equilibrium problems. These algorithms can be viewed as a extension of the paper title, the extragradient algorithm with inertial effects for solving the variational inequality proposed by Dong et al. (Optimization 65:2217–2226, 2016. 10.1080/02331934.2016.1239266). The weak convergence of the first algorithm is well established based on the standard assumption imposed on the cost bifunction. We provide a strong convergence for the second algorithm without knowing the strongly pseudomonoton and the Lipschitz-type constants of cost bifunction. The practical interpretation of a second algorithm is that the algorithm uses a sequence of step sizes that is converging to zero and non-summable. Numerical examples are used to assist the well-established convergence result, and we see that the suggested algorithm has a competitive advantage over time of execution and the number of iterations. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01018205
- Volume :
- 39
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Computational & Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 142370054
- Full Text :
- https://doi.org/10.1007/s40314-020-1093-0