Geodesic
On an algorithm of bilateral restrictions smoothing with spline
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 19 (2016) no. 3, pp. 331-342

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In this paper, the problem of constructing a spline $\sigma$ in the Hilbert space satisfying bilateral restrictions $z^-\le A\sigma\le z^+$ with a linear operator $A$ and minimizing a squared Hilbert seminorm is studied. A solution to this problem could be obtained with the convex programming iterative methods, in particular, with the gradient projection method. A modification of the gradient projection method allowing one to reveal a set of active restrictions in a smaller number of iterations is offered. The efficiency of the modification proposed is shown on the problem of approximation with a pseudo-linear bivariate spline. 
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     author = {A. I. Rozhenko and E. A. Fedorov},
     title = {On an algorithm of bilateral restrictions smoothing with spline},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {331--342},
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     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2016_19_3_a6/}
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A. I. Rozhenko; E. A. Fedorov. On an algorithm of bilateral restrictions smoothing with spline. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 19 (2016) no. 3, pp. 331-342. http://geodesic.mathdoc.fr/item/SJVM_2016_19_3_a6/