TY - JOUR
T1 - Primal-Dual Path-Following Methods and the Trust-Region Updating Strategy for Linear Programming with Noisy Data
AU - Luo , Xinlong
AU - Yao , Yiyan
JO - Journal of Computational Mathematics
VL - 5
SP - 756
EP - 776
PY - 2022
DA - 2022/05
SN - 40
DO - http://doi.org/10.4208/jcm.2101-m2020-0173
UR - https://global-sci.org/intro/article_detail/jcm/20546.html
KW - Continuation Newton method, Trust-region method, Linear programming, Rank deficiency, Path-following method, Noisy data.
AB - <p style="text-align: justify;">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.</p>