Barriers and symmetric regularization of the Lagrange function in the analysis of improper linear programming problems

In this paper, the author continues his research on the modification and adaptation of classical methods of the central path in order to apply them to the analysis of improper problems of linear programming. In the new constructions presented in the paper, in contrast to those developed earlier, it becomes possible to apply second-order optimization methods. Moreover, there is no need to specify in advance the type of impropriety of the problem being solved. Convergence theorems for the constructed methods are given, a meaningful interpretation of the obtained generalized solution is provided, and the results of numerical experiments are presented.