Strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spaces
In this paper, we introduce a new algorithm for solving pseudomonotone variational inequalities with a Lipschitz-type condition in a real Hilbert space. The algorithm is constructed around two algorithms: the subgradient extragradient algorithm and the inertial algorithm. The proposed algorithm uses...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2021-05-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2021-0011 |
| _version_ | 1828426395878948864 |
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| author | Wairojjana Nopparat Pakkaranang Nuttapol Pholasa Nattawut |
| author_facet | Wairojjana Nopparat Pakkaranang Nuttapol Pholasa Nattawut |
| author_sort | Wairojjana Nopparat |
| collection | DOAJ |
| description | In this paper, we introduce a new algorithm for solving pseudomonotone variational inequalities with a Lipschitz-type condition in a real Hilbert space. The algorithm is constructed around two algorithms: the subgradient extragradient algorithm and the inertial algorithm. The proposed algorithm uses a new step size rule based on local operator information rather than its Lipschitz constant or any other line search scheme and functions without any knowledge of the Lipschitz constant of an operator. The strong convergence of the algorithm is provided. To determine the computational performance of our algorithm, some numerical results are presented. |
| first_indexed | 2024-12-10T16:45:30Z |
| format | Article |
| id | doaj.art-b043747aed5749e58eaac5136b309188 |
| institution | Directory Open Access Journal |
| issn | 2391-4661 |
| language | English |
| last_indexed | 2024-12-10T16:45:30Z |
| publishDate | 2021-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-b043747aed5749e58eaac5136b3091882022-12-22T01:41:05ZengDe GruyterDemonstratio Mathematica2391-46612021-05-0154111012810.1515/dema-2021-0011Strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spacesWairojjana Nopparat0Pakkaranang Nuttapol1Pholasa Nattawut2Applied 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, ThailandDepartment of Mathematics, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, ThailandSchool of Science, University of Phayao, Phayao 56000, ThailandIn this paper, we introduce a new algorithm for solving pseudomonotone variational inequalities with a Lipschitz-type condition in a real Hilbert space. The algorithm is constructed around two algorithms: the subgradient extragradient algorithm and the inertial algorithm. The proposed algorithm uses a new step size rule based on local operator information rather than its Lipschitz constant or any other line search scheme and functions without any knowledge of the Lipschitz constant of an operator. The strong convergence of the algorithm is provided. To determine the computational performance of our algorithm, some numerical results are presented.https://doi.org/10.1515/dema-2021-0011variational inequalitiesextragradient-like algorithmstrong convergence theoremlipschitz continuitypseudomonotone mapping65y0565k1568w1047h0547h10 |
| spellingShingle | Wairojjana Nopparat Pakkaranang Nuttapol Pholasa Nattawut Strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spaces Demonstratio Mathematica variational inequalities extragradient-like algorithm strong convergence theorem lipschitz continuity pseudomonotone mapping 65y05 65k15 68w10 47h05 47h10 |
| title | Strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spaces |
| title_full | Strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spaces |
| title_fullStr | Strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spaces |
| title_full_unstemmed | Strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spaces |
| title_short | Strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spaces |
| title_sort | strong convergence inertial projection algorithm with self adaptive step size rule for pseudomonotone variational inequalities in hilbert spaces |
| topic | variational inequalities extragradient-like algorithm strong convergence theorem lipschitz continuity pseudomonotone mapping 65y05 65k15 68w10 47h05 47h10 |
| url | https://doi.org/10.1515/dema-2021-0011 |
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