Dual active-set algorithm for optimal 3-monotone regression
The paper considers a shape-constrained optimization problem of constructing monotone regression which has gained much attention over the recent years. This paper presents the results of constructing the nonlinear regression with $3$-monotone constraints. Monotone regression of high orders can be ap...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Saratov State University
2022-05-01
|
| Series: | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
| Subjects: | |
| Online Access: | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2022/05/216-223-gudkov_et_al.pdf |
| _version_ | 1818242970087849984 |
|---|---|
| author | Gudkov, Alexandr A. Sidorov, Sergei Petrovich Spiridonov, Kirill A. |
| author_facet | Gudkov, Alexandr A. Sidorov, Sergei Petrovich Spiridonov, Kirill A. |
| author_sort | Gudkov, Alexandr A. |
| collection | DOAJ |
| description | The paper considers a shape-constrained optimization problem of constructing monotone regression which has gained much attention over the recent years. This paper presents the results of constructing the nonlinear regression with $3$-monotone constraints. Monotone regression of high orders can be applied in many fields, including non-parametric mathematical statistics and empirical data smoothing. In this paper, an iterative algorithm is proposed for constructing a sparse $3$-monotone regression, i.e. for finding a $3$-monotone vector with the lowest square error of approximation to a given (not necessarily $3$-monotone) vector. The problem can be written as a convex programming problem with linear constraints. It is proved that the proposed dual active-set algorithm has polynomial complexity and obtains the optimal solution. |
| first_indexed | 2024-12-12T13:53:41Z |
| format | Article |
| id | doaj.art-548cfa405f5347fe99ee96416dbc96ba |
| institution | Directory Open Access Journal |
| issn | 1816-9791 2541-9005 |
| language | English |
| last_indexed | 2024-12-12T13:53:41Z |
| publishDate | 2022-05-01 |
| publisher | Saratov State University |
| record_format | Article |
| series | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
| spelling | doaj.art-548cfa405f5347fe99ee96416dbc96ba2022-12-22T00:22:30ZengSaratov State UniversityИзвестия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика1816-97912541-90052022-05-0122221622310.18500/1816-9791-2022-22-2-216-223Dual active-set algorithm for optimal 3-monotone regressionGudkov, Alexandr A.0Sidorov, Sergei Petrovich1Spiridonov, Kirill A.2Saratov State University, Russia, 410026, Saratov, Astrahanskaya str., 83Saratov State University, Russia, 410026, Saratov, Astrahanskaya str., 83Saratov State University, Russia, 410026, Saratov, Astrahanskaya str., 83The paper considers a shape-constrained optimization problem of constructing monotone regression which has gained much attention over the recent years. This paper presents the results of constructing the nonlinear regression with $3$-monotone constraints. Monotone regression of high orders can be applied in many fields, including non-parametric mathematical statistics and empirical data smoothing. In this paper, an iterative algorithm is proposed for constructing a sparse $3$-monotone regression, i.e. for finding a $3$-monotone vector with the lowest square error of approximation to a given (not necessarily $3$-monotone) vector. The problem can be written as a convex programming problem with linear constraints. It is proved that the proposed dual active-set algorithm has polynomial complexity and obtains the optimal solution.https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2022/05/216-223-gudkov_et_al.pdfdual algorithmisotonic regressionmonotone regressionk-monotone regressionconvex regression |
| spellingShingle | Gudkov, Alexandr A. Sidorov, Sergei Petrovich Spiridonov, Kirill A. Dual active-set algorithm for optimal 3-monotone regression Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика dual algorithm isotonic regression monotone regression k-monotone regression convex regression |
| title | Dual active-set algorithm for optimal 3-monotone regression |
| title_full | Dual active-set algorithm for optimal 3-monotone regression |
| title_fullStr | Dual active-set algorithm for optimal 3-monotone regression |
| title_full_unstemmed | Dual active-set algorithm for optimal 3-monotone regression |
| title_short | Dual active-set algorithm for optimal 3-monotone regression |
| title_sort | dual active set algorithm for optimal 3 monotone regression |
| topic | dual algorithm isotonic regression monotone regression k-monotone regression convex regression |
| url | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2022/05/216-223-gudkov_et_al.pdf |
| work_keys_str_mv | AT gudkovalexandra dualactivesetalgorithmforoptimal3monotoneregression AT sidorovsergeipetrovich dualactivesetalgorithmforoptimal3monotoneregression AT spiridonovkirilla dualactivesetalgorithmforoptimal3monotoneregression |