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: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Saratov State University
2022-05-01
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| 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 |
| Summary: | 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. |
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| ISSN: | 1816-9791 2541-9005 |