A new class of inertial algorithms with monotonic step sizes for solving fixed point and variational inequalities
This study presents two inertial type extragradient algorithms for finding a common solution to the monotone variational inequalities and fixed point problems for ρ$$ \rho $$‐demicontractive mapping in real Hilbert spaces. We provide inertial type iterative algorithms with self‐adaptive variable ste...
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| Published in | Mathematical methods in the applied sciences Vol. 45; no. 16; pp. 9061 - 9088 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Freiburg
Wiley Subscription Services, Inc
15.11.2022
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| Online Access | Get full text |
| ISSN | 0170-4214 1099-1476 |
| DOI | 10.1002/mma.8293 |
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| Abstract | This study presents two inertial type extragradient algorithms for finding a common solution to the monotone variational inequalities and fixed point problems for
ρ$$ \rho $$‐demicontractive mapping in real Hilbert spaces. We provide inertial type iterative algorithms with self‐adaptive variable step size rules that do not require prior knowledge of the operator value. Our algorithms employ a basic step size rule, which is derived by certain computations at each iteration. Without previous knowledge of the operators Lipschitz constant, two strong convergence theorems were obtained. Finally, we present a number of numerical experiments to evaluate the efficacy and applicability of the proposed algorithms. The conclusions of this study on variational inequality and fixed point problems support and extend previous findings. |
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| AbstractList | This study presents two inertial type extragradient algorithms for finding a common solution to the monotone variational inequalities and fixed point problems for
ρ$$ \rho $$‐demicontractive mapping in real Hilbert spaces. We provide inertial type iterative algorithms with self‐adaptive variable step size rules that do not require prior knowledge of the operator value. Our algorithms employ a basic step size rule, which is derived by certain computations at each iteration. Without previous knowledge of the operators Lipschitz constant, two strong convergence theorems were obtained. Finally, we present a number of numerical experiments to evaluate the efficacy and applicability of the proposed algorithms. The conclusions of this study on variational inequality and fixed point problems support and extend previous findings. This study presents two inertial type extragradient algorithms for finding a common solution to the monotone variational inequalities and fixed point problems for ‐demicontractive mapping in real Hilbert spaces. We provide inertial type iterative algorithms with self‐adaptive variable step size rules that do not require prior knowledge of the operator value. Our algorithms employ a basic step size rule, which is derived by certain computations at each iteration. Without previous knowledge of the operators Lipschitz constant, two strong convergence theorems were obtained. Finally, we present a number of numerical experiments to evaluate the efficacy and applicability of the proposed algorithms. The conclusions of this study on variational inequality and fixed point problems support and extend previous findings. This study presents two inertial type extragradient algorithms for finding a common solution to the monotone variational inequalities and fixed point problems for ρ$$ \rho $$‐demicontractive mapping in real Hilbert spaces. We provide inertial type iterative algorithms with self‐adaptive variable step size rules that do not require prior knowledge of the operator value. Our algorithms employ a basic step size rule, which is derived by certain computations at each iteration. Without previous knowledge of the operators Lipschitz constant, two strong convergence theorems were obtained. Finally, we present a number of numerical experiments to evaluate the efficacy and applicability of the proposed algorithms. The conclusions of this study on variational inequality and fixed point problems support and extend previous findings. |
| Author | Kumam, Wiyada Kumam, Poom Sombut, Kamonrat Rehman, Habib ur |
| Author_xml | – sequence: 1 givenname: Habib ur orcidid: 0000-0003-2659-8226 surname: Rehman fullname: Rehman, Habib ur organization: King Mongkut's University of Technology Thonburi (KMUTT) – sequence: 2 givenname: Poom orcidid: 0000-0002-5463-4581 surname: Kumam fullname: Kumam, Poom email: poom.kum@kmutt.ac.th organization: China Medical University Hospital, China Medical University – sequence: 3 givenname: Wiyada surname: Kumam fullname: Kumam, Wiyada organization: Rajamangala University of Technology Thanyaburi (RMUTT) – sequence: 4 givenname: Kamonrat surname: Sombut fullname: Sombut, Kamonrat organization: Rajamangala University of Technology Thanyaburi (RMUTT) |
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| Cites_doi | 10.1016/S0377-2217(02)00290-4 10.23952/jnfa.2020.35 10.1080/02331934.2010.539689 10.1081/NFA-200045815 10.1137/1029059 10.1007/s11075-017-0468-9 10.1137/080716542 10.1007/s10957-013-0494-2 10.1080/02331930701762829 10.1007/s12190‐021‐01576‐z 10.1137/S0363012998338806 10.1007/978-1-4757-3005-0_1 10.1007/s10898-019-00834-6 10.1515/9783110667097 10.1007/s10898-017-0506-0 10.1007/s10589-016-9857-6 10.1016/j.na.2011.09.005 10.1016/0041-5553(64)90137-5 10.1007/s10598-010-9057-7 10.1007/s11075-017-0412-z 10.1007/s10957-010-9757-3 10.1007/s43036-021-00155-0 10.1137/060675319 10.1006/jmaa.1999.6615 10.1007/s10589-019-00124-7 10.1007/s11075-017-0452-4 10.1090/S0002-9939-1953-0054846-3 10.1137/S0363012997317475 10.1080/02331939708844365 |
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| SubjectTerms | Adaptive algorithms fixed point problem Fixed points (mathematics) Hilbert space Inequalities inertial algorithms Iterative algorithms Iterative methods Mathematical analysis strong convergence theorems subgradient extragradient algorithm Tseng's extragradient algorithm variational inequalities |
| Title | A new class of inertial algorithms with monotonic step sizes for solving fixed point and variational inequalities |
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