Variance reduced moving balls approximation method for smooth constrained minimization problems
In this paper, we consider the problem of minimizing the sum of a large number of smooth convex functions subject to a complicated constraint set defined by a smooth convex function. Such a problem has wide applications in many areas, such as machine learning and signal processing. By utilizing vari...
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| Published in | Optimization letters Vol. 18; no. 5; pp. 1253 - 1271 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Springer Berlin Heidelberg
01.06.2024
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| ISSN | 1862-4472 1862-4480 |
| DOI | 10.1007/s11590-023-02049-x |
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| Abstract | In this paper, we consider the problem of minimizing the sum of a large number of smooth convex functions subject to a complicated constraint set defined by a smooth convex function. Such a problem has wide applications in many areas, such as machine learning and signal processing. By utilizing variance reduction and moving balls approximation techniques, we propose a new variance reduced moving balls approximation method. Compared with existing convergence rates of moving balls approximation-type methods that require the strong convexity of the objective function, a notable advantage of the proposed method is that the linear and sublinear convergence rates can be guaranteed under the quadratic gradient growth property and convexity condition, respectively. To demonstrate its effectiveness, numerical experiments for solving the smooth regularized logistic regression problem and the Neyman-Pearson classification problem are presented. |
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| AbstractList | In this paper, we consider the problem of minimizing the sum of a large number of smooth convex functions subject to a complicated constraint set defined by a smooth convex function. Such a problem has wide applications in many areas, such as machine learning and signal processing. By utilizing variance reduction and moving balls approximation techniques, we propose a new variance reduced moving balls approximation method. Compared with existing convergence rates of moving balls approximation-type methods that require the strong convexity of the objective function, a notable advantage of the proposed method is that the linear and sublinear convergence rates can be guaranteed under the quadratic gradient growth property and convexity condition, respectively. To demonstrate its effectiveness, numerical experiments for solving the smooth regularized logistic regression problem and the Neyman-Pearson classification problem are presented. |
| Author | Tu, Kai Yang, Zhichun Xia, Fu-quan |
| Author_xml | – sequence: 1 givenname: Zhichun surname: Yang fullname: Yang, Zhichun organization: School of Mathematical Science, Sichuan Normal University – sequence: 2 givenname: Fu-quan surname: Xia fullname: Xia, Fu-quan organization: School of Mathematical Science, Sichuan Normal University – sequence: 3 givenname: Kai orcidid: 0000-0002-0557-6792 surname: Tu fullname: Tu, Kai email: kaitu_02@163.com organization: College of Mathematics and Statistics, Shenzhen University, School of Mathematical Science, Laurent Mathematics Center, Sichuan Normal University |
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| Cites_doi | 10.1002/wics.1376 10.1287/moor.2015.0735 10.1080/10618600.2018.1473777 10.1007/s10107-004-0552-5 10.1007/s12532-021-00214-w 10.1137/1.9781611974997 10.1007/s10107-017-1206-8 10.1137/090763317 10.1137/16M1080173 10.1137/20M1314057 10.1214/aoms/1177729586 10.1007/s11590-014-0795-x 10.1007/s10107-019-01425-9 10.1007/s11590-019-01520-y 10.1137/070704277 10.1007/978-3-319-91578-4 10.1007/978-1-4757-4296-1 10.1109/ICASSP.2017.7952918 10.4208/jcm.1912-m2016-0634 10.1007/s10107-018-1232-1 10.1007/s11590-020-01550-x |
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| Keywords | Convergence rate Smooth constrained minimization Moving balls approximation Relaxed strong convexity condition Variance reduction |
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| Title | Variance reduced moving balls approximation method for smooth constrained minimization problems |
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