Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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

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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

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Dual active-set algorithm for optimal 3-monotone regression

Gudkov Alexandr A., Saratov State University
Sidorov Sergei Petrovich, Saratov State University
Spiridonov Kirill A., Saratov State University

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.

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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