New inertial proximal gradient methods for unconstrained convex optimization problems
The proximal gradient method is a highly powerful tool for solving the composite convex optimization problem. In this paper, firstly, we propose inexact inertial acceleration methods based on the viscosity approximation and proximal scaled gradient algorithm to accelerate the convergence of the algo...
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| Vydáno v: | Journal of inequalities and applications Ročník 2020; číslo 1; s. 1 - 18 |
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| Jazyk: | angličtina |
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Cham
Springer International Publishing
07.12.2020
Springer Nature B.V SpringerOpen |
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| ISSN: | 1029-242X, 1025-5834, 1029-242X |
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| Abstract | The proximal gradient method is a highly powerful tool for solving the composite convex optimization problem. In this paper, firstly, we propose inexact inertial acceleration methods based on the viscosity approximation and proximal scaled gradient algorithm to accelerate the convergence of the algorithm. Under reasonable parameters, we prove that our algorithms strongly converge to some solution of the problem, which is the unique solution of a variational inequality problem. Secondly, we propose an inexact alternated inertial proximal point algorithm. Under suitable conditions, the weak convergence theorem is proved. Finally, numerical results illustrate the performances of our algorithms and present a comparison with related algorithms. Our results improve and extend the corresponding results reported by many authors recently. |
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| AbstractList | The proximal gradient method is a highly powerful tool for solving the composite convex optimization problem. In this paper, firstly, we propose inexact inertial acceleration methods based on the viscosity approximation and proximal scaled gradient algorithm to accelerate the convergence of the algorithm. Under reasonable parameters, we prove that our algorithms strongly converge to some solution of the problem, which is the unique solution of a variational inequality problem. Secondly, we propose an inexact alternated inertial proximal point algorithm. Under suitable conditions, the weak convergence theorem is proved. Finally, numerical results illustrate the performances of our algorithms and present a comparison with related algorithms. Our results improve and extend the corresponding results reported by many authors recently. Abstract The proximal gradient method is a highly powerful tool for solving the composite convex optimization problem. In this paper, firstly, we propose inexact inertial acceleration methods based on the viscosity approximation and proximal scaled gradient algorithm to accelerate the convergence of the algorithm. Under reasonable parameters, we prove that our algorithms strongly converge to some solution of the problem, which is the unique solution of a variational inequality problem. Secondly, we propose an inexact alternated inertial proximal point algorithm. Under suitable conditions, the weak convergence theorem is proved. Finally, numerical results illustrate the performances of our algorithms and present a comparison with related algorithms. Our results improve and extend the corresponding results reported by many authors recently. |
| ArticleNumber | 255 |
| Author | Zhang, Yiqun Bu, Qinxiong Duan, Peichao |
| Author_xml | – sequence: 1 givenname: Peichao surname: Duan fullname: Duan, Peichao email: pcduancauc@126.com organization: College of Science, Tianjin Key Lab for Advanced Signal Processing, Civil Aviation University of China – sequence: 2 givenname: Yiqun surname: Zhang fullname: Zhang, Yiqun organization: College of Science, Civil Aviation University of China – sequence: 3 givenname: Qinxiong surname: Bu fullname: Bu, Qinxiong organization: College of Science, Civil Aviation University of China |
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| Cites_doi | 10.1007/s11590-011-0418-8 10.1007/s10589-015-9777-x 10.1186/s13660-015-0857-3 10.1186/s13660-016-1242-6 10.1088/1361-6420/33/4/044008 10.1007/s10957-011-9837-z 10.1080/10556788.2017.1396601 10.1111/j.1475-3995.2009.00695.x 10.1016/j.jmaa.2006.06.055 10.1137/080716542 10.1017/CBO9780511526152 10.1088/0266-5611/27/4/045009 10.1186/s13660-018-1695-x 10.1016/0041-5553(64)90137-5 10.1088/0266-5611/26/6/065008 10.19139/124 10.1007/s11590-020-01603-1 |
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| Snippet | The proximal gradient method is a highly powerful tool for solving the composite convex optimization problem. In this paper, firstly, we propose inexact... Abstract The proximal gradient method is a highly powerful tool for solving the composite convex optimization problem. In this paper, firstly, we propose... |
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| SubjectTerms | Algorithms Alternated inertial acceleration Analysis Applications of Mathematics Computational geometry Convergence Convex analysis Convex optimization Convexity Inertial acceleration Mathematics Mathematics and Statistics Optimization Proximal operator Viscosity approximation |
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| Title | New inertial proximal gradient methods for unconstrained convex optimization problems |
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