One modification of the logarithmic barrier function method in linear and convex programming

A novel modification of the logarithmic barrier function method is introduced for solving problems of linear and convex programming. The modification is based on a parametric shifting of the constraints of the original problem, similarly to what was done in the method of Wierzbicki–Hestenes–Powell multipliers for the usual quadratic penalty function (this method is also known as the method of modified Lagrange functions). The new method is described, its convergence is proved, and results of numerical experiments are given.