Inexact proximal gradient algorithm with random reshuffling for nonsmooth optimization
Proximal gradient algorithms are popularly implemented to achieve convex optimization with nonsmooth regularization. Obtaining the exact solution of the proximal operator for nonsmooth regularization is challenging because errors exist in the computation of the gradient; consequently, the design and...
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| Veröffentlicht in: | Science China. Information sciences Jg. 68; H. 1; S. 112201 |
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| Sprache: | Englisch |
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Beijing
Science China Press
01.01.2025
Springer Nature B.V |
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| ISSN: | 1674-733X, 1869-1919 |
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| Abstract | Proximal gradient algorithms are popularly implemented to achieve convex optimization with nonsmooth regularization. Obtaining the exact solution of the proximal operator for nonsmooth regularization is challenging because errors exist in the computation of the gradient; consequently, the design and application of inexact proximal gradient algorithms have attracted considerable attention from researchers. This paper proposes computationally efficient basic and inexact proximal gradient descent algorithms with random reshuffling. The proposed stochastic algorithms take randomly reshuffled data to perform successive gradient descents and implement only one proximal operator after all data pass through. We prove the convergence results of the proposed proximal gradient algorithms under the sampling-without-replacement reshuffling scheme. When computational errors exist in gradients and proximal operations, the proposed inexact proximal gradient algorithms can converge to an optimal solution neighborhood. Finally, we apply the proposed algorithms to compressed sensing and compare their efficiency with some popular algorithms. |
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| AbstractList | Proximal gradient algorithms are popularly implemented to achieve convex optimization with nonsmooth regularization. Obtaining the exact solution of the proximal operator for nonsmooth regularization is challenging because errors exist in the computation of the gradient; consequently, the design and application of inexact proximal gradient algorithms have attracted considerable attention from researchers. This paper proposes computationally efficient basic and inexact proximal gradient descent algorithms with random reshuffling. The proposed stochastic algorithms take randomly reshuffled data to perform successive gradient descents and implement only one proximal operator after all data pass through. We prove the convergence results of the proposed proximal gradient algorithms under the sampling-without-replacement reshuffling scheme. When computational errors exist in gradients and proximal operations, the proposed inexact proximal gradient algorithms can converge to an optimal solution neighborhood. Finally, we apply the proposed algorithms to compressed sensing and compare their efficiency with some popular algorithms. |
| ArticleNumber | 112201 |
| Author | Jiang, Xia Chen, Jie Sun, Jian Zeng, Xianlin Fang, Yanyan |
| Author_xml | – sequence: 1 givenname: Xia surname: Jiang fullname: Jiang, Xia organization: National Key Lab of Autonomous Intelligent Unmanned Systems, School of Automation, Beijing Institute of Technology – sequence: 2 givenname: Yanyan surname: Fang fullname: Fang, Yanyan organization: National Key Lab of Autonomous Intelligent Unmanned Systems, School of Automation, Beijing Institute of Technology – sequence: 3 givenname: Xianlin surname: Zeng fullname: Zeng, Xianlin email: xianlin.zeng@bit.edu.cn organization: National Key Lab of Autonomous Intelligent Unmanned Systems, School of Automation, Beijing Institute of Technology – sequence: 4 givenname: Jian surname: Sun fullname: Sun, Jian organization: National Key Lab of Autonomous Intelligent Unmanned Systems, School of Automation, Beijing Institute of Technology, Chongqing Innovation Center, Beijing Institute of Technology – sequence: 5 givenname: Jie surname: Chen fullname: Chen, Jie organization: Chongqing Innovation Center, Beijing Institute of Technology, School of Electronic and Information Engineering, Tongji University |
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| Cites_doi | 10.1007/s10107-019-01440-w 10.1137/18M1207685 10.1109/TAC.2023.3293521 10.1007/s10589-017-9932-7 10.1007/s11432-018-9588-0 10.1137/080716542 10.1109/JAS.2022.105602 10.1137/S1052623499362111 10.1007/s11432-017-9246-3 10.1007/s11432-010-0110-0 10.1109/TAC.2020.3009363 10.1561/2200000016 10.1002/cpa.20132 10.1109/TCYB.2016.2546965 10.1109/JAS.2023.123441 10.1109/TCYB.2018.2883566 10.1109/JSTSP.2007.910281 10.1016/j.laa.2010.09.020 10.1007/s00245-019-09617-7 10.1002/cpa.20042 10.1007/s11432-021-3319-4 10.1137/110837711 10.1007/s11432-020-3148-x 10.1109/TIP.2022.3155949 10.1007/s12532-014-0074-y 10.1016/j.ins.2017.03.023 10.1007/s10107-013-0677-5 10.1109/TSP.2015.2461520 10.1109/TIT.2007.909108 |
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| Keywords | compressed sensing inexact computation nonsmooth optimization proximal operator random reshuffling |
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| Snippet | Proximal gradient algorithms are popularly implemented to achieve convex optimization with nonsmooth regularization. Obtaining the exact solution of the... |
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| Title | Inexact proximal gradient algorithm with random reshuffling for nonsmooth optimization |
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