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Scientific Part
Computer Sciences
Dual active-set algorithm for optimal 3-monotone regression
A. A. Gudkov, S. P. Sidorov, K. A. Spiridonov Saratov State University, 83 Astrakhanskaya St., Saratov 410012, Russia
Abstract:
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.
Key words:
dual algorithm, isotonic regression, monotone regression, $k$-monotone regression, convex regression.
Received: 03.12.2021 Accepted: 15.01.2022
Citation:
A. A. Gudkov, S. P. Sidorov, K. A. Spiridonov, “Dual active-set algorithm for optimal 3-monotone regression”, Izv. Saratov Univ. Math. Mech. Inform., 22:2 (2022), 216–223
Linking options:
https://www.mathnet.ru/eng/isu935 https://www.mathnet.ru/eng/isu/v22/i2/p216
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Abstract page: | 92 | Full-text PDF : | 33 | References: | 30 |
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