Convergence analysis and applications of the inertial algorithm solving inclusion problems
Nonlinear operator theory is an important area of nonlinear functional analysis. This area encompasses diverse nonlinear problems in many areas of mathematics, the physical sciences and engineering such as monotone operator equations, fixed point problems and more. In this work we are concern with t...
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| Published in | Applied numerical mathematics Vol. 175; pp. 1 - 17 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.05.2022
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0168-9274 1873-5460 |
| DOI | 10.1016/j.apnum.2022.01.016 |
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| Abstract | Nonlinear operator theory is an important area of nonlinear functional analysis. This area encompasses diverse nonlinear problems in many areas of mathematics, the physical sciences and engineering such as monotone operator equations, fixed point problems and more.
In this work we are concern with the problem of finding a common solution of a monotone operator equation and fixed point of a nonexpansive mapping in real Hilbert spaces. Derived from dynamical systems, a simple inertial forward-backward splitting method for solving the problem is presented and analyzed under mild and standard assumptions. Some numerical examples in real-world and comparisons with related works, illustrate the theoretical advantages as well the potential applicability of the proposed scheme. |
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| AbstractList | Nonlinear operator theory is an important area of nonlinear functional analysis. This area encompasses diverse nonlinear problems in many areas of mathematics, the physical sciences and engineering such as monotone operator equations, fixed point problems and more.
In this work we are concern with the problem of finding a common solution of a monotone operator equation and fixed point of a nonexpansive mapping in real Hilbert spaces. Derived from dynamical systems, a simple inertial forward-backward splitting method for solving the problem is presented and analyzed under mild and standard assumptions. Some numerical examples in real-world and comparisons with related works, illustrate the theoretical advantages as well the potential applicability of the proposed scheme. |
| Author | Je Cho, Yeol Lin, Honghua Gibali, Aviv Tang, Yan |
| Author_xml | – sequence: 1 givenname: Yan orcidid: 0000-0003-4086-0040 surname: Tang fullname: Tang, Yan email: ttyy7999@163.com organization: School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China – sequence: 2 givenname: Honghua surname: Lin fullname: Lin, Honghua email: 654740672@qq.com organization: Business School, Southwest University of Political Science and Law, Chongqing 401120, China – sequence: 3 givenname: Aviv surname: Gibali fullname: Gibali, Aviv email: avivg@braude.ac.il organization: Department of Mathematics, ORT Braude College, Karmiel 2161002, Israel – sequence: 4 givenname: Yeol surname: Je Cho fullname: Je Cho, Yeol email: yjchomath@gmail.com organization: Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Republic of Korea |
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| Cites_doi | 10.1007/s10851-014-0523-2 10.1006/jmaa.1993.1309 10.3390/math7020167 10.1016/j.apnum.2021.02.004 10.1137/S0363012998338806 10.1007/s10898-018-0727-x 10.1090/S0002-9947-1956-0084194-4 10.1080/02331930412331327157 10.1080/00036818608839641 10.1112/S0024610702003332 10.1007/s11590-016-1102-9 10.1090/S0002-9904-1967-11761-0 10.1007/s11228-008-0102-z 10.1137/120872802 10.1215/S0012-7094-62-02933-2 10.1080/02331934.2019.1702040 10.1016/j.jmaa.2005.12.066 10.1090/S0002-9904-1967-11823-8 10.1017/S144678870002807X 10.1007/s11075-017-0462-2 10.1080/02331934.2014.883510 10.1016/j.apnum.2020.06.009 10.1137/130910294 10.1007/s11590-013-0629-2 10.1023/A:1011253113155 10.1007/s10288-020-00440-3 10.1007/s11784-017-0464-7 10.1007/s10898-017-0506-0 10.1007/s10957-011-9814-6 10.1080/00036810701556144 10.1080/00036811.2016.1157589 10.1007/s11075-011-9490-5 10.1080/02331934.2020.1783260 |
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| Keywords | Inertial technique Monotone operator equation Forward-backward algorithm Nonexpansive mapping Fixed point |
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