A method of adding–removing knots for solving smoothing problems with obstacles

We study a method of adding–removing knots that has been proposed in the literature for solving the smoothing problem with obstacles. The method uses the coefficients of natural splines in the expansion by radial basis functions. We present examples of cycling and counterexamples to possible use of some ideas. We also give some sufficient conditions for finiteness of the method.     

Connection Between Smoothing Problems with Obstacles and Weights

We study how to reduce the smoothing problems with obstacles to the solution of smoothing problems with weights. We prove that, for problems with obstacles in Hilbert spaces, and in the classical case, especially, in several variable problems, the associated Lagrangian has a saddle point. This implies the existence of equivalent problems with weights.