A modified inertial proximal minimization algorithm for structured nonconvex and nonsmooth problem
We introduce an enhanced inertial proximal minimization algorithm tailored for a category of structured nonconvex and nonsmooth optimization problems. The objective function in question is an aggregation of a smooth function with an associated linear operator, a nonsmooth function dependent on an in...
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| Published in: | Journal of inequalities and applications Vol. 2024; no. 1; pp. 124 - 23 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Cham
Springer International Publishing
20.09.2024
Springer Nature B.V SpringerOpen |
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| ISSN: | 1029-242X, 1025-5834, 1029-242X |
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| Abstract | We introduce an enhanced inertial proximal minimization algorithm tailored for a category of structured nonconvex and nonsmooth optimization problems. The objective function in question is an aggregation of a smooth function with an associated linear operator, a nonsmooth function dependent on an independent variable, and a mixed function involving two variables. Throughout the iterative procedure, parameters are selected employing a straightforward approach, and weak inertial terms are incorporated into two subproblems within the update sequence. Under a set of lenient conditions, we demonstrate that the sequence engendered by our algorithm is bounded. Furthermore, we establish the global and strong convergence of the algorithmic sequence, contingent upon the assumption that the principal function adheres to the Kurdyka–Łojasiewicz (KL) property. Ultimately, the numerical outcomes corroborate the algorithm’s feasibility and efficacy. |
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| AbstractList | We introduce an enhanced inertial proximal minimization algorithm tailored for a category of structured nonconvex and nonsmooth optimization problems. The objective function in question is an aggregation of a smooth function with an associated linear operator, a nonsmooth function dependent on an independent variable, and a mixed function involving two variables. Throughout the iterative procedure, parameters are selected employing a straightforward approach, and weak inertial terms are incorporated into two subproblems within the update sequence. Under a set of lenient conditions, we demonstrate that the sequence engendered by our algorithm is bounded. Furthermore, we establish the global and strong convergence of the algorithmic sequence, contingent upon the assumption that the principal function adheres to the Kurdyka–Łojasiewicz (KL) property. Ultimately, the numerical outcomes corroborate the algorithm’s feasibility and efficacy. We introduce an enhanced inertial proximal minimization algorithm tailored for a category of structured nonconvex and nonsmooth optimization problems. The objective function in question is an aggregation of a smooth function with an associated linear operator, a nonsmooth function dependent on an independent variable, and a mixed function involving two variables. Throughout the iterative procedure, parameters are selected employing a straightforward approach, and weak inertial terms are incorporated into two subproblems within the update sequence. Under a set of lenient conditions, we demonstrate that the sequence engendered by our algorithm is bounded. Furthermore, we establish the global and strong convergence of the algorithmic sequence, contingent upon the assumption that the principal function adheres to the Kurdyka–Łojasiewicz (KL) property. Ultimately, the numerical outcomes corroborate the algorithm’s feasibility and efficacy. Abstract We introduce an enhanced inertial proximal minimization algorithm tailored for a category of structured nonconvex and nonsmooth optimization problems. The objective function in question is an aggregation of a smooth function with an associated linear operator, a nonsmooth function dependent on an independent variable, and a mixed function involving two variables. Throughout the iterative procedure, parameters are selected employing a straightforward approach, and weak inertial terms are incorporated into two subproblems within the update sequence. Under a set of lenient conditions, we demonstrate that the sequence engendered by our algorithm is bounded. Furthermore, we establish the global and strong convergence of the algorithmic sequence, contingent upon the assumption that the principal function adheres to the Kurdyka–Łojasiewicz (KL) property. Ultimately, the numerical outcomes corroborate the algorithm’s feasibility and efficacy. |
| ArticleNumber | 124 |
| Author | Ma, Qianfeng Xue, Zhonghui |
| Author_xml | – sequence: 1 givenname: Zhonghui surname: Xue fullname: Xue, Zhonghui email: hnlgxzh@163.com organization: Shanghai Publishing and Printing College – sequence: 2 givenname: Qianfeng surname: Ma fullname: Ma, Qianfeng organization: Shanghai Publishing and Printing College |
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| Cites_doi | 10.1007/s10107-011-0484-9 10.1109/TIT.2006.871582 10.1287/moor.2019.1008 10.1137/14095697X 10.1007/s10915-010-9408-8 10.1186/s13660-017-1504-y 10.1016/0167-2789(92)90242-F 10.1109/ACCESS.2019.2914461 10.1007/s10957-015-0730-z 10.1137/18M1190689 10.1287/moor.1100.0449 10.1088/1361-6420/ac0966 10.1023/A:1017501703105 10.1137/S0363012998338806 10.1007/s10898-019-00819-5 10.1007/BF01397082 10.1007/s10107-013-0701-9 10.1137/140998135 10.1137/0716071 10.1137/16M1064064 10.1080/00207160.2020.1812585 10.1016/0041-5553(64)90137-5 10.1007/s10898-022-01176-6 10.1137/050626090 10.1137/140980910 10.1007/s10851-015-0565-0 10.1007/s10915-018-0757-z 10.1090/S0025-5718-2012-02598-1 |
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| StartPage | 124 |
| SubjectTerms | Algorithms Analysis Applications of Mathematics Approximation Dependent variables Independent variables Kurdyka–Łojasiewicz property Linear operators Mathematics Mathematics and Statistics Nonconvex-nonsmooth optimization Optimization Parameter modification Proximal minimization algorithm Weak inertial |
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| Title | A modified inertial proximal minimization algorithm for structured nonconvex and nonsmooth problem |
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| Volume | 2024 |
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