On the adaptation of the least squares method to improper problems of mathematical programming

We propose a modification of the least squares method, which allows to apply this method not only to usual feasible problems but also to improper problems of mathematical programming of the first kind. The method constructs the usual solution for feasible problems and a generalized solution for improper problems; the generalized solution has a very useful meaningful interpretation. We describe the algorithm, characterize the generalized solution, prove convergence theorems, and present results of numerical experiments.