AN INTERIOR POINT CONTINUOUS PATH-FOLLOWING TRAJECTORY FOR LINEAR PROGRAMMING
AN INTERIOR POINT CONTINUOUS PATH-FOLLOWING TRAJECTORY FOR LINEAR PROGRAMMING
复制标题
线性规划的内部点连续路径跟踪轨迹
DOI：
10.3934/jimo.2018107
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发表时间：
2019
影响因子：
1.3
通讯作者：
Li-Zhi Liao
中科院分区：
文献类型：
--
作者：
Liming Sun;Li-Zhi Liao
本文提出了一种线性规划的内点连续路径跟踪轨迹。我们连续轨迹中的下降方向可以被看作线性规划的缩放方向和中心方向的某种组合。我们的内点连续路径跟踪轨迹的一个关键组成部分是一个常微分方程（ODE）系统。详细分析和讨论了该常微分方程组解的各种性质，包括极限收敛性。还提供了几个说明性的例子来证明这种连续轨迹的数值行为。
In this paper, an interior point continuous path-following trajectory is proposed for linear programming. The descent direction in our continuous trajectory can be viewed as some combination of the ane scaling direction and the centering direction for linear programming. A key component in our interior point continuous path-following trajectory is an ordinary differential equation (ODE) system. Various properties including the convergence in the limit for the solution of this ODE system are analyzed and discussed in detail. Several illustrative examples are also provided to demonstrate the numerical behavior of this continuous trajectory.