论文标题
带有噪声数据的线性编程的原始双偶路遵循方法和线性编程的信任区域更新策略
Primal-dual path-following methods and the trust-region updating strategy for linear programming with noisy data
论文作者
论文摘要
在本文中，我们考虑了标准线性编程问题的原始偶型路径遵循方法和信任区域更新策略。对于小嘈杂数据的排名缺陷问题，我们还基于QR分解的列枢转提供了预处理方法。然后，当初始点严格可行时，我们证明了新方法的全局收敛性。最后，对于有或没有Netlib集合中的小嘈杂数据的一些等级缺陷的问题，我们将其与其他两种流行的内点方法进行了比较，即MATLAB环境的subroutine Pathfollow.m和内置的subroutine linprog.m。数值结果表明，对于小噪声数据而言，新方法比其他两种方法更强大。
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.
