A three-operator splitting algorithm with deviations for generalized DC programming
In this paper, we introduce a three-operator splitting algorithm with deviations for solving the minimization problem composed of the sum of two convex functions minus a convex and smooth function in a real Hilbert space. The main feature of the proposed method is that two per-iteration deviation ve...
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| Vydáno v: | Applied numerical mathematics Ročník 191; s. 62 - 74 |
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| Jazyk: | angličtina |
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Elsevier B.V
01.09.2023
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| ISSN: | 0168-9274 |
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| Abstract | In this paper, we introduce a three-operator splitting algorithm with deviations for solving the minimization problem composed of the sum of two convex functions minus a convex and smooth function in a real Hilbert space. The main feature of the proposed method is that two per-iteration deviation vectors provide additional degrees of freedom. We propose one-step and two step inertial three-operator splitting algorithms by selecting the deviations along a momentum direction. A numerical experiment for DC regularized sparse recovery problems shows that the proposed algorithms have better performance than the original three-operator splitting algorithm. |
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| AbstractList | In this paper, we introduce a three-operator splitting algorithm with deviations for solving the minimization problem composed of the sum of two convex functions minus a convex and smooth function in a real Hilbert space. The main feature of the proposed method is that two per-iteration deviation vectors provide additional degrees of freedom. We propose one-step and two step inertial three-operator splitting algorithms by selecting the deviations along a momentum direction. A numerical experiment for DC regularized sparse recovery problems shows that the proposed algorithms have better performance than the original three-operator splitting algorithm. |
| Author | Hu, Ziyue Dong, Qiao-Li |
| Author_xml | – sequence: 1 givenname: Ziyue surname: Hu fullname: Hu, Ziyue email: ziyuehumath@163.com – sequence: 2 givenname: Qiao-Li orcidid: 0000-0001-6765-4437 surname: Dong fullname: Dong, Qiao-Li email: dongql@lsec.cc.ac.cn |
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| Cites_doi | 10.1137/20M1326775 10.1007/s10915-022-01845-4 10.1007/s10589-017-9954-1 10.1007/s11228-017-0421-z 10.1016/j.ins.2020.08.038 10.1080/02331934.2019.1625354 10.1007/s10107-017-1181-0 10.1007/s10898-021-01079-y 10.1080/02331934.2017.1296838 10.1561/2200000016 10.1007/s10915-017-0463-2 10.1090/S0002-9947-1956-0084194-4 10.1007/s10898-011-9703-4 10.1137/140952363 10.1007/s10898-019-00828-4 10.1137/120872802 10.24193/fpt-ro.2019.2.30 10.1109/TCOMM.2021.3107582 10.1007/s10107-018-1286-0 10.1007/s11590-019-01482-1 10.1007/s10898-018-0727-x 10.1016/j.ejor.2014.11.031 10.1137/18M1214342 10.1007/s10589-019-00067-z |
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| Keywords | Three-operator splitting algorithm Difference-of-convex programming Deviations Inertial algorithms |
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