On solving pseudomonotone equilibrium problems via two new extragradient-type methods under convex constraints
The primary objective of this study is to develop two new proximal-type algorithms for solving equilibrium problems in real Hilbert space. Both new algorithms are analogous to the well-known two-step extragradient algorithm for solving the variational inequality problem in Hilbert spaces. The propos...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2022-08-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2022-0025 |
| _version_ | 1818025398386032640 |
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| author | Khunpanuk Chainarong Pakkaranang Nuttapol Pholasa Nattawut |
| author_facet | Khunpanuk Chainarong Pakkaranang Nuttapol Pholasa Nattawut |
| author_sort | Khunpanuk Chainarong |
| collection | DOAJ |
| description | The primary objective of this study is to develop two new proximal-type algorithms for solving equilibrium problems in real Hilbert space. Both new algorithms are analogous to the well-known two-step extragradient algorithm for solving the variational inequality problem in Hilbert spaces. The proposed iterative algorithms use a new step size rule based on local bifunction information instead of the line search technique. Two weak convergence theorems for both algorithms are well-established by letting mild conditions. The main results are used to solve the fixed point and variational inequality problems. Finally, we present several computational experiments to demonstrate the efficiency and effectiveness of the proposed algorithms. |
| first_indexed | 2024-12-10T04:15:28Z |
| format | Article |
| id | doaj.art-a5334b97f35b483d95f2f6c9a37c6b01 |
| institution | Directory Open Access Journal |
| issn | 2391-4661 |
| language | English |
| last_indexed | 2024-12-10T04:15:28Z |
| publishDate | 2022-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-a5334b97f35b483d95f2f6c9a37c6b012022-12-22T02:02:37ZengDe GruyterDemonstratio Mathematica2391-46612022-08-0155129731410.1515/dema-2022-0025On solving pseudomonotone equilibrium problems via two new extragradient-type methods under convex constraintsKhunpanuk Chainarong0Pakkaranang Nuttapol1Pholasa Nattawut2Mathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, ThailandMathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, ThailandSchool of Science, University of Phayao, Phayao 56000, ThailandThe primary objective of this study is to develop two new proximal-type algorithms for solving equilibrium problems in real Hilbert space. Both new algorithms are analogous to the well-known two-step extragradient algorithm for solving the variational inequality problem in Hilbert spaces. The proposed iterative algorithms use a new step size rule based on local bifunction information instead of the line search technique. Two weak convergence theorems for both algorithms are well-established by letting mild conditions. The main results are used to solve the fixed point and variational inequality problems. Finally, we present several computational experiments to demonstrate the efficiency and effectiveness of the proposed algorithms.https://doi.org/10.1515/dema-2022-0025equilibrium problemlipschitz-type continuousweak convergence theorempseudomonotone bifunctionproximal algorithm47h0647h0947j0547j25 |
| spellingShingle | Khunpanuk Chainarong Pakkaranang Nuttapol Pholasa Nattawut On solving pseudomonotone equilibrium problems via two new extragradient-type methods under convex constraints Demonstratio Mathematica equilibrium problem lipschitz-type continuous weak convergence theorem pseudomonotone bifunction proximal algorithm 47h06 47h09 47j05 47j25 |
| title | On solving pseudomonotone equilibrium problems via two new extragradient-type methods under convex constraints |
| title_full | On solving pseudomonotone equilibrium problems via two new extragradient-type methods under convex constraints |
| title_fullStr | On solving pseudomonotone equilibrium problems via two new extragradient-type methods under convex constraints |
| title_full_unstemmed | On solving pseudomonotone equilibrium problems via two new extragradient-type methods under convex constraints |
| title_short | On solving pseudomonotone equilibrium problems via two new extragradient-type methods under convex constraints |
| title_sort | on solving pseudomonotone equilibrium problems via two new extragradient type methods under convex constraints |
| topic | equilibrium problem lipschitz-type continuous weak convergence theorem pseudomonotone bifunction proximal algorithm 47h06 47h09 47j05 47j25 |
| url | https://doi.org/10.1515/dema-2022-0025 |
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