On parameter control in iterative linear programming methods based on a new class of smooth exterior penalty functions

New results are presented on the construction of exterior penalty functions of increased smoothness in linear programming and on the construction of iterative methods on their basis with automatic matching of their parameters. New constructions, similarly to interior penalty functions, make it possible to use second-order optimization methods and at the same time do not require knowledge of at least one interior admissible point of the original problem for the start of the operation. Moreover, the new penalty functions can also be applied to improper linear programming problems (problems with inconsistent constraint systems), for which they can produce generalized (compromise) solutions. Convergence theorems are proved and data of numerical experiments are presented.