A fast computational Gauss–Seidel type iPALM algorithm using an incremental aggregated gradient strategy for weakly convex composite optimization problems with application in image processing
In this paper, we propose a Gauss–Seidel type inertial proximal alternating linearized minimization method with incremental aggregated gradient (IAG-GiPALM) for solving a class of nonconvex and nonsmooth composite optimization problems, whose objective function is the sum of a finite number of smoot...
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| Vydáno v: | Journal of computational and applied mathematics Ročník 474; s. 116973 |
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| Jazyk: | angličtina |
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Elsevier B.V
01.03.2026
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| ISSN: | 0377-0427 |
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| Abstract | In this paper, we propose a Gauss–Seidel type inertial proximal alternating linearized minimization method with incremental aggregated gradient (IAG-GiPALM) for solving a class of nonconvex and nonsmooth composite optimization problems, whose objective function is the sum of a finite number of smooth nonconvex functions and nonsmooth weakly convex functions. This new algorithm inherits the advantages of the Gauss–Seidel type inertial proximal alternating linearized minimization method (GiPALM) and the incremental aggregated proximal method. Under some mild conditions, we prove that any limit point of the sequence generated by IAG-GiPALM is a critical point of the optimization problems. Moreover, we establish the global convergence and convergence rate of the algorithm under the Kurdyka-Łojasiewicz property. In addition, some numerical results are conducted to demonstrate the efficiency of the new method. |
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| AbstractList | In this paper, we propose a Gauss–Seidel type inertial proximal alternating linearized minimization method with incremental aggregated gradient (IAG-GiPALM) for solving a class of nonconvex and nonsmooth composite optimization problems, whose objective function is the sum of a finite number of smooth nonconvex functions and nonsmooth weakly convex functions. This new algorithm inherits the advantages of the Gauss–Seidel type inertial proximal alternating linearized minimization method (GiPALM) and the incremental aggregated proximal method. Under some mild conditions, we prove that any limit point of the sequence generated by IAG-GiPALM is a critical point of the optimization problems. Moreover, we establish the global convergence and convergence rate of the algorithm under the Kurdyka-Łojasiewicz property. In addition, some numerical results are conducted to demonstrate the efficiency of the new method. |
| ArticleNumber | 116973 |
| Author | Hou, Junru Liu, Zhiyu Jia, Zehui Dong, Ping |
| Author_xml | – sequence: 1 givenname: Zehui orcidid: 0000-0003-2774-4854 surname: Jia fullname: Jia, Zehui email: jiazehui90@126.com organization: Department of Information and Computing Science, School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, PR China – sequence: 2 givenname: Junru surname: Hou fullname: Hou, Junru organization: School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, PR China – sequence: 3 givenname: Ping surname: Dong fullname: Dong, Ping organization: School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, PR China – sequence: 4 givenname: Zhiyu surname: Liu fullname: Liu, Zhiyu organization: School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, PR China |
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| Cites_doi | 10.1137/040615961 10.1287/moor.1100.0449 10.1137/140983938 10.1007/s10107-020-01599-7 10.1198/106186006X113430 10.1287/moor.2019.0992 10.1137/16M1078604 10.1137/21M140376X 10.1007/s10107-007-0133-5 10.1137/20M1387213 10.1007/s10898-021-01044-9 10.1016/j.apnum.2023.03.014 10.1007/s10957-021-01880-5 10.1137/120887795 10.1137/17M1124085 10.1214/aoms/1177729586 10.1007/s10957-019-01538-3 10.1145/1970392.1970395 10.1137/16M1064064 10.1137/16M1094415 10.1287/moor.2019.1047 10.1007/s10107-013-0701-9 10.1007/s10898-019-00819-5 10.1007/s10589-021-00286-3 10.1137/21M1432661 10.1007/s43670-022-00021-x 10.1007/s10915-017-0376-0 |
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| Keywords | Proximal alternating linearized minimization Nonconvex optimization Kurdyka-Łojasiewicz property Incremental aggregated proximal method |
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| Snippet | In this paper, we propose a Gauss–Seidel type inertial proximal alternating linearized minimization method with incremental aggregated gradient (IAG-GiPALM)... |
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| StartPage | 116973 |
| SubjectTerms | Incremental aggregated proximal method Kurdyka-Łojasiewicz property Nonconvex optimization Proximal alternating linearized minimization |
| Title | A fast computational Gauss–Seidel type iPALM algorithm using an incremental aggregated gradient strategy for weakly convex composite optimization problems with application in image processing |
| URI | https://dx.doi.org/10.1016/j.cam.2025.116973 |
| Volume | 474 |
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