On the convergence of a modified barrier function method for convex quadratic and linear programming

We analyze convergence properties of the Modified Barrier Function Method (MBFM), which operates like the usual Augmented Lagrangian method, except that it uses a shifted logarithmic barrier function in place of the usual quadratic penalty function. The MBFM avoids some of the drawbacks of classical barrier methods. The convergence of the MBFM had previously been established under strict regularity assumptions for general convex programs. We focus on Convex Quadratic and Linear Programs and strengthen substantially the existing convergence results. For Linear Programs, we also analyze the speed of convergence of the dual sequence.