The weight coefficients in the weighted least squares method

We consider the problem of estimating parameters of linear mathematical models. It is proved that due to the choice of weights in the least squares method it is possible to obtain solutions by minimizing any penalty functions of a wide class, including those of the Hölder norms. A limitation on a set of solutions resulting from the variation of the weights in the least squares method has been determined. The possibility of the practical use of the established theoretical facts is illustrated by the ecology-mathematical models.