Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Gudkov A. A., Sidorov S. P., Spiridonov K. A. Dual active-set algorithm for optimal 3-monotone regression. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2022, vol. 22, iss. 2, pp. 216-223. DOI: 10.18500/1816-9791-2022-22-2-216-223, EDN: MEHLKW

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
31.05.2022
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Language: 
English
Heading: 
Computer Sciences
Article type: 
Article
UDC: 
519.85
DOI: 
10.18500/1816-9791-2022-22-2-216-223
EDN: 
MEHLKW

Dual active-set algorithm for optimal 3-monotone regression

Autors: 
Gudkov Alexandr A., Saratov State University
Sidorov Sergei Petrovich, Saratov State University
Spiridonov Kirill A., Saratov State University
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
Acknowledgments: 
This work was supported by the Ministry of science and education of the Russian Federation in the framework of the basic part of the scientific research state task (project FSRR-2020-0006).
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Received: 
03.12.2021
Accepted: 
15.01.2022
Published: 
31.05.2022
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