Quadratic rate of convergence for a primal-dual exponential penalty algorithm

We study a primal-dual path following method for mathematical programming problems, based on an exponential penalty function suitably adapted to handle equality as well as inequality constraints. The primal-dual approach avoids the ill-conditioning associated with the primal exponential penalty method. Moreover, under strong second order sufficient conditions we prove that the method has a quadratic rate of convergence, improving the known results for primal methods based on the exponential penalty.