Primal-dual path-following methods and the trust-region updating strategy for linear programming with noisy data
This work addresses robustness in linear programming for noisy, rank-deficient data, but it is incremental as it builds on existing interior-point methods.
The paper tackles linear programming problems with noisy data by proposing a primal-dual path-following method with a trust-region updating strategy and a QR-based preprocessing technique for rank-deficient cases. Numerical results on NETLIB problems show the new method is more robust than two existing interior-point methods for rank-deficient problems with small noise.
In this article, we consider the primal-dual path-following method and the trust-region updating strategy for the standard linear programming problem. For the rank-deficient problem with the small noisy data, we also give the preprocessing method based on the QR decomposition with column pivoting. Then, we prove the global convergence of the new method when the initial point is strictly primal-dual feasible. Finally, for some rank-deficient problems with or without the small noisy data from the NETLIB collection, we compare it with other two popular interior-point methods, i.e. the subroutine pathfollow.m and the built-in subroutine linprog.m of the MATLAB environment. Numerical results show that the new method is more robust than the other two methods for the rank-deficient problem with the small noise data.