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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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/

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