Accelerated Subgradient Extragradient Algorithm for Solving Bilevel System of Equilibrium Problems
In this research paper, we propose a novel approach termed the inertial subgradient extragradient algorithm to solve bilevel system equilibrium problems within the realm of real Hilbert spaces. Our algorithm is capable of circumventing the necessity for prior knowledge about the Lipschitz constant o...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/9/1681 |
| _version_ | 1797576652537987072 |
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| author | Somyot Plubtieng Tadchai Yuying |
| author_facet | Somyot Plubtieng Tadchai Yuying |
| author_sort | Somyot Plubtieng |
| collection | DOAJ |
| description | In this research paper, we propose a novel approach termed the inertial subgradient extragradient algorithm to solve bilevel system equilibrium problems within the realm of real Hilbert spaces. Our algorithm is capable of circumventing the necessity for prior knowledge about the Lipschitz constant of the involving bifunction and only computes the minimization of strong bifunctions onto the feasible set that is required. Under appropriate conditions, we establish strong convergence theorems for our proposed algorithms. To validate our algorithms, we illustrate a series of numerical examples. Through these examples, we demonstrate the performance of the algorithms we have put forth in this paper. |
| first_indexed | 2024-03-10T21:54:52Z |
| format | Article |
| id | doaj.art-c9697cc48aec480cace2050ec9878df1 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T21:54:52Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-c9697cc48aec480cace2050ec9878df12023-11-19T13:11:09ZengMDPI AGSymmetry2073-89942023-08-01159168110.3390/sym15091681Accelerated Subgradient Extragradient Algorithm for Solving Bilevel System of Equilibrium ProblemsSomyot Plubtieng0Tadchai Yuying1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandDepartment of Mathematics, Uttaradit Rajabhat University, Uttaradit 53000, ThailandIn this research paper, we propose a novel approach termed the inertial subgradient extragradient algorithm to solve bilevel system equilibrium problems within the realm of real Hilbert spaces. Our algorithm is capable of circumventing the necessity for prior knowledge about the Lipschitz constant of the involving bifunction and only computes the minimization of strong bifunctions onto the feasible set that is required. Under appropriate conditions, we establish strong convergence theorems for our proposed algorithms. To validate our algorithms, we illustrate a series of numerical examples. Through these examples, we demonstrate the performance of the algorithms we have put forth in this paper.https://www.mdpi.com/2073-8994/15/9/1681bilevel system of equilibrium problemsinertial methodsubgradient extragradient algorithm and monotone operator |
| spellingShingle | Somyot Plubtieng Tadchai Yuying Accelerated Subgradient Extragradient Algorithm for Solving Bilevel System of Equilibrium Problems Symmetry bilevel system of equilibrium problems inertial method subgradient extragradient algorithm and monotone operator |
| title | Accelerated Subgradient Extragradient Algorithm for Solving Bilevel System of Equilibrium Problems |
| title_full | Accelerated Subgradient Extragradient Algorithm for Solving Bilevel System of Equilibrium Problems |
| title_fullStr | Accelerated Subgradient Extragradient Algorithm for Solving Bilevel System of Equilibrium Problems |
| title_full_unstemmed | Accelerated Subgradient Extragradient Algorithm for Solving Bilevel System of Equilibrium Problems |
| title_short | Accelerated Subgradient Extragradient Algorithm for Solving Bilevel System of Equilibrium Problems |
| title_sort | accelerated subgradient extragradient algorithm for solving bilevel system of equilibrium problems |
| topic | bilevel system of equilibrium problems inertial method subgradient extragradient algorithm and monotone operator |
| url | https://www.mdpi.com/2073-8994/15/9/1681 |
| work_keys_str_mv | AT somyotplubtieng acceleratedsubgradientextragradientalgorithmforsolvingbilevelsystemofequilibriumproblems AT tadchaiyuying acceleratedsubgradientextragradientalgorithmforsolvingbilevelsystemofequilibriumproblems |