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A new extragradient algorithm with adaptive step-size for solving split equilibrium problems.
- Source :
-
Journal of Inequalities & Applications . 8/2/2021, Vol. 2021 Issue 1, p1-14. 14p. - Publication Year :
- 2021
-
Abstract
- He (J. Inequal. Appl. 2012:Article ID 162 2012) introduced the proximal point CQ algorithm (PPCQ) for solving the split equilibrium problem (SEP). However, the PPCQ converges weakly to a solution of the SEP and is restricted to monotone bifunctions. In addition, the step-size used in the PPCQ is a fixed constant μ in the interval (0 , 1 ∥ A ∥ 2) . This often leads to excessive numerical computation in each iteration, which may affect the applicability of the PPCQ. In order to overcome these intrinsic drawbacks, we propose a robust step-size { μ n } n = 1 ∞ which does not require computation of ∥ A ∥ and apply the adaptive step-size rule on { μ n } n = 1 ∞ in such a way that it adjusts itself in accordance with the movement of associated components of the algorithm in each iteration. Then, we introduce a self-adaptive extragradient-CQ algorithm (SECQ) for solving the SEP and prove that our proposed SECQ converges strongly to a solution of the SEP with more general pseudomonotone equilibrium bifunctions. Finally, we present a preliminary numerical test to demonstrate that our SECQ outperforms the PPCQ. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGORITHMS
Subjects
Details
- Language :
- English
- ISSN :
- 10255834
- Volume :
- 2021
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Inequalities & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 151703974
- Full Text :
- https://doi.org/10.1186/s13660-021-02668-x