How to Use Barriers and Symmetric Regularization of Lagrange Function in Analysis of Improper Nonlinear Programming Problems

In the note, we present a new approach to numerical analysis of improper mathematical programming problems based on ideas of symmetrically regularization of their Lagrange functions, additionally equipped with barrier terms for both groups of variables, primal and dual. It makes it possibly not to specify in advance the type of incorrectness of the problem being solved as well as apply second-order optimization methods for them. The description of the approach, convergence theorems and meaningful interpretation of the obtained generalized solutions are given.