Modified Inertial Forward–Backward Algorithm in Banach Spaces and Its Application
In this paper, we present a new modified inertial forward–backward algorithm for finding a common solution of the quasi-variational inclusion problem and the variational inequality problem in a q-uniformly smooth Banach space. The proposed algorithm is based on descent, splitting and inertial ideas....
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| Veröffentlicht in: | Mathematics (Basel) Jg. 9; H. 12; S. 1365 |
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01.06.2021
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| Abstract | In this paper, we present a new modified inertial forward–backward algorithm for finding a common solution of the quasi-variational inclusion problem and the variational inequality problem in a q-uniformly smooth Banach space. The proposed algorithm is based on descent, splitting and inertial ideas. Under suitable assumptions, we prove that the sequence generated by the iterative algorithm converges strongly to the unique solution of the abovementioned problems. Numerical examples are also given to demonstrate our results. |
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| AbstractList | In this paper, we present a new modified inertial forward–backward algorithm for finding a common solution of the quasi-variational inclusion problem and the variational inequality problem in a q-uniformly smooth Banach space. The proposed algorithm is based on descent, splitting and inertial ideas. Under suitable assumptions, we prove that the sequence generated by the iterative algorithm converges strongly to the unique solution of the abovementioned problems. Numerical examples are also given to demonstrate our results. |
| Author | Postolache, Mihai Song, Yanlai |
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| Cites_doi | 10.1186/1687-1812-2012-65 10.1016/j.camwa.2009.09.003 10.1007/978-3-642-99970-3 10.1137/050626090 10.1007/s10851-014-0523-2 10.1007/s10898-012-9990-4 10.1007/s40065-018-0236-2 10.1023/A:1011253113155 10.1016/j.ejor.2011.01.042 10.3390/math8030447 10.1137/0314056 10.1287/moor.1.2.97 10.1007/978-1-4419-9467-7 10.1016/0022-247X(73)90024-3 10.1186/s13663-015-0335-0 10.1137/S0363012998338806 10.1016/j.jmaa.2004.04.059 10.1007/s10915-021-01428-9 10.1155/2012/109236 10.1016/0362-546X(91)90200-K 10.1287/moor.26.2.248.10558 |
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| Copyright | 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| SubjectTerms | Algorithms Banach space Banach spaces forward–backward method Hilbert space hybrid steepest decent method Iterative algorithms Iterative methods Mathematics quasi-variational inclusion problem variational inequality problem |
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| Title | Modified Inertial Forward–Backward Algorithm in Banach Spaces and Its Application |
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