  We present a primal-dual majorization-minimization method for solving
large-scale linear programs. A smooth barrier augmented Lagrangian (SBAL)
function with strict convexity for the dual linear program is derived. The
majorization-minimization approach is naturally introduced to develop the
smoothness and convexity of the SBAL function. Our method only depends on a
factorization of the constant matrix independent of iterations and does not
need any computation on step sizes, thus can be expected to be particularly
appropriate for large-scale linear programs. The method shares some similar
properties to the first-order methods for linear programs, but its convergence
analysis is established on the differentiability and convexity of our SBAL
function. The global convergence is analyzed without prior requiring either the
primal or dual linear program to be feasible. Under the regular conditions, our
method is proved to be globally linearly convergent, and a new iteration
complexity result is given.
