Parallel Extragradient-Proximal Methods for Split Equilibrium Problems
In this paper, we introduce two parallel extragradient-proximal methods for solving split equilibrium problems. The algorithms combine the extragradient method, the proximal method and the shrinking projection method. The weak and strong convergence theorems for iterative sequences generated by the...
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| Published in | Mathematical modelling and analysis Vol. 21; no. 4; pp. 478 - 501 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Taylor & Francis
03.07.2016
Vilnius Gediminas Technical University |
| Subjects | |
| Online Access | Get full text |
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| Abstract | In this paper, we introduce two parallel extragradient-proximal methods for solving split equilibrium problems. The algorithms combine the extragradient method, the proximal method and the shrinking projection method. The weak and strong convergence theorems for iterative sequences generated by the algorithms are established under widely used assumptions for equilibrium bifunctions. We also present an application to split variational inequality problems and a numerical example to illustrate the convergence of the proposed algorithms. |
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| AbstractList | In this paper, we introduce two parallel extragradient-proximal methods for solving split equilibrium problems. The algorithms combine the extragradient method, the proximal method and the shrinking projection method. The weak and strong convergence theorems for iterative sequences generated by the algorithms are established under widely used assumptions for equilibrium bifunctions. We also present an application to split variational inequality problems and a numerical example to illustrate the convergence of the proposed algorithms.Keywords: equilibrium problem, split equilibrium problem, extragradient method, proximal method, parallel algorithm.AMS Subject Classification: 90C33, 68W10, 65K10. In this paper, we introduce two parallel extragradient-proximal methods for solving split equilibrium problems. The algorithms combine the extragradient method, the proximal method and the shrinking projection method. The weak and strong convergence theorems for iterative sequences generated by the algorithms are established under widely used assumptions for equilibrium bifunctions. We also present an application to split variational inequality problems and a numerical example to illustrate the convergence of the proposed algorithms. |
| Audience | Academic |
| Author | Hieua, Dang Van |
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| SubjectTerms | Algorithms Convergence Convergence (Mathematics) equilibrium problem extragradient method Functions (Mathematics) Inequalities Iterative methods Mathematical models Mathematical research parallel algorithm Projection proximal method Sequences Sequences (Mathematics) split equilibrium problem Theorems |
| Title | Parallel Extragradient-Proximal Methods for Split Equilibrium Problems |
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