Geodesic
Dual active-set algorithm for optimal 3-monotone regression
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 22 (2022) no. 2, pp. 216-223

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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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     author = {A. A. Gudkov and S. P. Sidorov and K. A. Spiridonov},
     title = {Dual active-set algorithm for optimal 3-monotone regression},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
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     url = {http://geodesic.mathdoc.fr/item/ISU_2022_22_2_a7/}
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A. A. Gudkov; S. P. Sidorov; K. A. Spiridonov. Dual active-set algorithm for optimal 3-monotone regression. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 22 (2022) no. 2, pp. 216-223. http://geodesic.mathdoc.fr/item/ISU_2022_22_2_a7/