Analysis of the convergence of a class of barrier projection methods for linear programming problems (Q1571244)

The author considers the continuous and discrete versions of the barrier projection method for solving direct and inverse linear programming problems. Local and nonlocal properties of these methods are analyzed. It is proved that, for the barrier functions of the form \(x^p\), solutions to the direct and inverse problems are asymptotically stable equilibrium states of the corresponding systems for odd values of the parameter \(p\). All versions of the method are locally convergent on \(\mathbb{R}^n_+\).