Geodesic
Analysis of the convergence of the algorithm for constructing a convex regression dependence
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 2, Tome 200 (2021), pp. 115-125

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In this paper, to solve the problem of constructing a convex approximation to noisy data, we propose an algorithm for constructing convex regression using the active set approach. It is shown that the algorithm converges to the optimal solution and it is found the estimate of its complexity.
Keywords: nonlinear optimization, active set
Mots-clés : monotonic regression, convex regression, segment regression. 
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     author = {A. A. Gudkov and S. P. Sidorov and K. A. Spiridonov},
     title = {Analysis of the convergence of the algorithm for constructing a convex regression dependence},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {115--125},
     publisher = {mathdoc},
     volume = {200},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_200_a12/}
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A. A. Gudkov; S. P. Sidorov; K. A. Spiridonov. Analysis of the convergence of the algorithm for constructing a convex regression dependence. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 2, Tome 200 (2021), pp. 115-125. http://geodesic.mathdoc.fr/item/INTO_2021_200_a12/