On the Algorithm of Smoothing by a Spline with Bilateral Constraints

In this paper, the problem of constructing a spline sigma in the Hilbert space, which satisfies the bilateral constraints z(-) <= A sigma <= z(+) with a linear operator A and minimizes the squared Hilbert seminorm is studied. A solution to this problem can be obtained with convex programming iterative methods, in particular, with the gradient projection method. A modification of the gradient projection method is proposed, which allows one to find a set of active constraints with a smaller number of iterations. The efficiency of the modification proposed is demonstrated in the problem of approximation with a pseudolinear bivariate spline.