Primal-Dual Path-Following Methods and the Trust-Region Updating Strategy for Linear Programming with Noisy Data
Year: 2022
Author: Xinlong Luo, Yiyan Yao
Journal of Computational Mathematics, Vol. 40 (2022), Iss. 5 : pp. 756–776
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2101-m2020-0173
Journal of Computational Mathematics, Vol. 40 (2022), Iss. 5 : pp. 756–776
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Continuation Newton method Trust-region method Linear programming Rank deficiency Path-following method Noisy data.