  Powerful interior-point methods (IPM) based commercial solvers, such as
Gurobi and Mosek, have been hugely successful in solving large-scale linear
programming (LP) problems. The high efficiency of these solvers depends
critically on the sparsity of the problem data and advanced matrix
factorization techniques. For a large scale LP problem with data matrix $A$
that is dense (possibly structured) or whose corresponding normal matrix $AA^T$
has a dense Cholesky factor (even with re-ordering), these solvers may require
excessive computational cost and/or extremely heavy memory usage in each
interior-point iteration. Unfortunately, the natural remedy, i.e., the use of
iterative methods based IPM solvers, although can avoid the explicit
computation of the coefficient matrix and its factorization, is not practically
viable due to the inherent extreme ill-conditioning of the large scale normal
equation arising in each interior-point iteration. To provide a better
alternative choice for solving large scale LPs with dense data or requiring
expensive factorization of its normal equation, we propose a semismooth Newton
based inexact proximal augmented Lagrangian ({\sc Snipal}) method. Different
from classical IPMs, in each iteration of {\sc Snipal}, iterative methods can
efficiently be used to solve simpler yet better conditioned semismooth Newton
linear systems. Moreover, {\sc Snipal} not only enjoys a fast asymptotic
superlinear convergence but is also proven to enjoy a finite termination
property. Numerical comparisons with Gurobi have demonstrated encouraging
potential of {\sc Snipal} for handling large-scale LP problems where the
constraint matrix $A$ has a dense representation or $AA^T$ has a dense
factorization even with an appropriate re-ordering.
