Two-step inertial forward-reflected-backward splitting based algorithm for nonconvex mixed variational inequalities
This paper presents a modification of a recently studied Malitsky–Tam forward-reflected-backward splitting method with two-step inertial extrapolation to solve nonconvex mixed variational inequalities. We give global convergence results and nonasymptotic O(1/k) convergence rate of our proposed metho...
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| Veröffentlicht in: | Journal of computational and applied mathematics Jg. 426; S. 115093 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Elsevier B.V
01.07.2023
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| ISSN: | 0377-0427, 1879-1778 |
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| Abstract | This paper presents a modification of a recently studied Malitsky–Tam forward-reflected-backward splitting method with two-step inertial extrapolation to solve nonconvex mixed variational inequalities. We give global convergence results and nonasymptotic O(1/k) convergence rate of our proposed method under some appropriate conditions and present some mathematical justifications. |
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| AbstractList | This paper presents a modification of a recently studied Malitsky–Tam forward-reflected-backward splitting method with two-step inertial extrapolation to solve nonconvex mixed variational inequalities. We give global convergence results and nonasymptotic O(1/k) convergence rate of our proposed method under some appropriate conditions and present some mathematical justifications. |
| ArticleNumber | 115093 |
| Author | Izuchukwu, Chinedu Dong, Qiao-Li Shehu, Yekini |
| Author_xml | – sequence: 1 givenname: Chinedu surname: Izuchukwu fullname: Izuchukwu, Chinedu email: chinedu.izuchukwu@wits.ac.za organization: School of Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg, 2050, South Africa – sequence: 2 givenname: Yekini orcidid: 0000-0001-9224-7139 surname: Shehu fullname: Shehu, Yekini email: yekini.shehu@zjnu.edu.cn organization: Department of Mathematics, Zhejiang Normal University, Jinhua 321004, People’s Republic of China – sequence: 3 givenname: Qiao-Li surname: Dong fullname: Dong, Qiao-Li email: dongql@lsec.cc.ac.cn organization: College of Science, Civil Aviation University of China, Tianjin, 300300, People’s Republic of China |
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| Cites_doi | 10.1007/s10898-018-0727-x 10.1137/080716542 10.1137/18M1207260 10.1007/s10898-011-9752-8 10.1137/140980910 10.1007/s10898-021-01081-4 10.1016/0041-5553(64)90137-5 10.1016/j.ejor.2015.05.041 10.1007/s10898-007-9243-0 10.1007/s10957-021-01860-9 10.1007/s10957-018-1321-6 10.1007/s10107-007-0124-6 10.1080/02331934.2017.1294592 10.1007/s10957-019-01548-1 10.1137/S0363012997317475 10.1007/978-3-662-12613-4 10.1023/A:1020848524253 10.1002/mma.5703 10.1007/s10107-019-01416-w |
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| Keywords | Nonconvex variational inequalities 68Q25 90C30 Proximal point algorithms 90C25 Two-step inertial extrapolation 90C22 Forward-reflected-backward splitting 90C60 49M25 |
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| References | Ricceri (b4) 2019; 3 Scaman, Virmaux (b27) 2018 Grad, Lara (b10) 2021; 190 Iusem, Lara (b11) 2019; 180 Muu, Nguyen, Quy (b8) 2008; 41 Boţ, Csetnek (b24) 2017; 66 Polyak (b17) 1964; 4 Nesterov (b18) 1983; 27 Hieu, Cho, Xiao (b28) 2019; 42 Malitsky (b7) 2020; 184 Jahn (b3) 2022; 4 Obukhovskii, Petrosyan, Wen, Bocharov (b5) 2022; 6 Polyak (b20) 1987 Hare, Sagastizábal (b25) 2009; 116 Noor (b12) 2002; 115 Iusem, Lara (b9) 2019; 183 Solodov, Svaiter (b26) 1999; 37 Grad, Lara (b16) 2022; 82 Noor, Huang (b13) 2012 Dong, Huang, Li, Cho, Rassias (b21) 2019; 73 Hadjisavvas, Komlosi, Schaible (b23) 2005 Chen, Ma, Yang (b6) 2015; 25 Berinde (b29) 2002 Glowinski, Lions, Trémolières (b2) 1981 Glowinski (b1) 1984 Langenberg, Tichatschke (b14) 2021; 52 Beck, Teboulle (b19) 2009; 2 Malitsky, Tam (b22) 2020; 30 Papa Quiroz, Mallma Ramirez, Oliveira (b15) 2015; 246 Glowinski (10.1016/j.cam.2023.115093_b2) 1981 Muu (10.1016/j.cam.2023.115093_b8) 2008; 41 Iusem (10.1016/j.cam.2023.115093_b9) 2019; 183 Noor (10.1016/j.cam.2023.115093_b13) 2012 Grad (10.1016/j.cam.2023.115093_b10) 2021; 190 Polyak (10.1016/j.cam.2023.115093_b17) 1964; 4 Boţ (10.1016/j.cam.2023.115093_b24) 2017; 66 Iusem (10.1016/j.cam.2023.115093_b11) 2019; 180 Papa Quiroz (10.1016/j.cam.2023.115093_b15) 2015; 246 Solodov (10.1016/j.cam.2023.115093_b26) 1999; 37 Dong (10.1016/j.cam.2023.115093_b21) 2019; 73 Noor (10.1016/j.cam.2023.115093_b12) 2002; 115 Berinde (10.1016/j.cam.2023.115093_b29) 2002 Polyak (10.1016/j.cam.2023.115093_b20) 1987 Jahn (10.1016/j.cam.2023.115093_b3) 2022; 4 Scaman (10.1016/j.cam.2023.115093_b27) 2018 Hadjisavvas (10.1016/j.cam.2023.115093_b23) 2005 Glowinski (10.1016/j.cam.2023.115093_b1) 1984 Malitsky (10.1016/j.cam.2023.115093_b22) 2020; 30 Nesterov (10.1016/j.cam.2023.115093_b18) 1983; 27 Beck (10.1016/j.cam.2023.115093_b19) 2009; 2 Hare (10.1016/j.cam.2023.115093_b25) 2009; 116 Langenberg (10.1016/j.cam.2023.115093_b14) 2021; 52 Malitsky (10.1016/j.cam.2023.115093_b7) 2020; 184 Ricceri (10.1016/j.cam.2023.115093_b4) 2019; 3 Obukhovskii (10.1016/j.cam.2023.115093_b5) 2022; 6 Hieu (10.1016/j.cam.2023.115093_b28) 2019; 42 Chen (10.1016/j.cam.2023.115093_b6) 2015; 25 Grad (10.1016/j.cam.2023.115093_b16) 2022; 82 |
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| Title | Two-step inertial forward-reflected-backward splitting based algorithm for nonconvex mixed variational inequalities |
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