An interior point method for solving systems of linear equations and inequalities

A simple interior point method is proposed for solving a system of linear equations subject to nonnegativity constraints. The direction of update is defined by projection of the current solution on a linear manifold defined by the equations. Infeasibility is discussed and extension for free and bounded variables is presented. As an application, we consider linear programming problems and a comparison with a state-of-the-art primal–dual infeasible interior point code is presented.