A nonparametric smoothing algorithm is proposed for evaluation of the function \(g:[a,b]\to R\) which minimizes \[ \sum_{i=1}^n (y_i-g(t_i))^2+\lambda\int_a^b (g^{(2)}(u))^2du \] under the constrains \(g^{(r)}(t)\geq 0\), \(\forall t\in[a,b]\). Here \((t_i,y_i)\) are the data points, \(g^{(k)}\) denotes derivatives of \(g\) with respect to \(t\), and \(r\) can be \(0,1,2\). In fact, the algorithm (based on quadratic programming techniques) is verifying the conditions only at points \(t_i\). Applications to real life data are considered.