PRIMAL-DUAL PATH-FOLLOWING METHODS AND THE TRUST-REGION UPDATING STRATEGY FOR LINEAR PROGRAMMING WITH NOISY DATA  

作　　者：Xinlong Luo Yiyan Yao 

机构地区：[1]School of Artificial Intelligence,Beijing University of Posts and Telecommunications,Beijing 100876,China

出　　处：《Journal of Computational Mathematics》2022年第5期756-776,共21页计算数学（英文）

基　　金：This work was supported in part by Grant 61876199 from National Natural Science Foundation of China,Grant YBWL2011085 from Huawei Technologies Co.,Ltd.,and Grant YJCB2011003HI;Innovation Research Program of Huawei Technologies Co.,Ltd..The first author is grateful to professor Li-Zhi Liao for introducing him the interiorpoint methods when he visited Hong Kong Baptist University in July,2012.

摘　　要：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 rankdeficient 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.

关 键 词：Continuation Newton method Trust-region method Linear programming Rank deficiency Path-following method Noisy data. 

分 类 号：O22[理学—运筹学与控制论]