Newton barrier: The maximum
number of iterations. While the simplex method usually performs a number of iterations which is proportional to the number of constraints (rows) in a problem, the barrier method standardly finds the optimal solution to a given accuracy after a number of iterations which is independent of the problem size. The penalty is rather that the time for each iteration increases with the size of the problem.
BARITERLIMIT specifies the maximum number of iterations which will be carried out by the barrier.