An Accelerated Extragradient Method for Solving Pseudomonotone Equilibrium Problems with Applications
Several methods have been put forward to solve equilibrium problems, in which the two-step extragradient method is very useful and significant. In this article, we propose a new extragradient-like method to evaluate the numerical solution of the pseudomonotone equilibrium in real Hilbert space. This...
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MDPI AG
2020-08-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/9/3/99 |
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| author | Nopparat Wairojjana Habib ur Rehman Ioannis K. Argyros Nuttapol Pakkaranang |
| author_facet | Nopparat Wairojjana Habib ur Rehman Ioannis K. Argyros Nuttapol Pakkaranang |
| author_sort | Nopparat Wairojjana |
| collection | DOAJ |
| description | Several methods have been put forward to solve equilibrium problems, in which the two-step extragradient method is very useful and significant. In this article, we propose a new extragradient-like method to evaluate the numerical solution of the pseudomonotone equilibrium in real Hilbert space. This method uses a non-monotonically stepsize technique based on local bifunction values and Lipschitz-type constants. Furthermore, we establish the weak convergence theorem for the suggested method and provide the applications of our results. Finally, several experimental results are reported to see the performance of the proposed method. |
| first_indexed | 2024-03-10T17:18:15Z |
| format | Article |
| id | doaj.art-679e38c051d34c2dbd7025d82a0c85cb |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T17:18:15Z |
| publishDate | 2020-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-679e38c051d34c2dbd7025d82a0c85cb2023-11-20T10:25:22ZengMDPI AGAxioms2075-16802020-08-01939910.3390/axioms9030099An Accelerated Extragradient Method for Solving Pseudomonotone Equilibrium Problems with ApplicationsNopparat Wairojjana0Habib ur Rehman1Ioannis K. Argyros2Nuttapol Pakkaranang3Applied Mathematics Program, Faculty of Science and Technology, Valaya Alongkorn Rajabhat University under the Royal Patronage (VRU), 1 Moo 20 Phaholyothin Road, Klong Neung, Klong Luang, Pathumthani 13180, ThailandKMUTTFixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, SCL 802 Fixed Point Laboratory, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandDepartment of Mathematical Sciences, Cameron University, Lawton, OK 73505, USAKMUTTFixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, SCL 802 Fixed Point Laboratory, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandSeveral methods have been put forward to solve equilibrium problems, in which the two-step extragradient method is very useful and significant. In this article, we propose a new extragradient-like method to evaluate the numerical solution of the pseudomonotone equilibrium in real Hilbert space. This method uses a non-monotonically stepsize technique based on local bifunction values and Lipschitz-type constants. Furthermore, we establish the weak convergence theorem for the suggested method and provide the applications of our results. Finally, several experimental results are reported to see the performance of the proposed method.https://www.mdpi.com/2075-1680/9/3/99Lipschitz-type conditionspseudomonotone bifunctionequilibrium problemvariational inequality problemsweak convergencefixed point problems |
| spellingShingle | Nopparat Wairojjana Habib ur Rehman Ioannis K. Argyros Nuttapol Pakkaranang An Accelerated Extragradient Method for Solving Pseudomonotone Equilibrium Problems with Applications Axioms Lipschitz-type conditions pseudomonotone bifunction equilibrium problem variational inequality problems weak convergence fixed point problems |
| title | An Accelerated Extragradient Method for Solving Pseudomonotone Equilibrium Problems with Applications |
| title_full | An Accelerated Extragradient Method for Solving Pseudomonotone Equilibrium Problems with Applications |
| title_fullStr | An Accelerated Extragradient Method for Solving Pseudomonotone Equilibrium Problems with Applications |
| title_full_unstemmed | An Accelerated Extragradient Method for Solving Pseudomonotone Equilibrium Problems with Applications |
| title_short | An Accelerated Extragradient Method for Solving Pseudomonotone Equilibrium Problems with Applications |
| title_sort | accelerated extragradient method for solving pseudomonotone equilibrium problems with applications |
| topic | Lipschitz-type conditions pseudomonotone bifunction equilibrium problem variational inequality problems weak convergence fixed point problems |
| url | https://www.mdpi.com/2075-1680/9/3/99 |
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