上海交通大学学报

上海交通大学学报（自然版） ›› 2012, Vol. 46 ›› Issue (10): 1701-1706.

• 数理科学和化学 • 上一篇    

一种线性不等式组的矩阵变换定解方法

刘道建1，2，黄天民1   

  1. (1.西南交通大学 电气工程学院，  成都 610031； 2.湖南科技大学 数学与计算科学学院， 湖南 湘潭 411201)  
  • 收稿日期:2012-03-26 出版日期:2012-10-30 发布日期:2012-10-30

A Matrix Column-Transform Solution-Decision Method for the System of Linear Inequalities

 LIU  Dao-Jian-1, 2 , HUANG  Tian-Min-1   

  1. (1.School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610036, China; 2.School of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan 411201, Hunan, China)
  • Received:2012-03-26 Online:2012-10-30 Published:2012-10-30

摘要： 通过构造一种关于线性不等式组的特殊矩阵——强迫性极点转移矩阵，以及定义一种特殊的矩阵运算——负旋转迭代运算，为解决不等式组的定解问题建立了一个崭新的数学平台，该平台较好地结合与反映了不等式组的线性与几何平面两面性特点，而且以该数学平台为基础提出了一种全新的不等式组定解方法.新定解方法将不等式组的定解过程转化成一系列矩阵初等列变换，定解操作简单快捷，结构化程度高，易程序化处理，便于在计算机上实现.此外，为了解决退化极点的转移问题，提出了单纯形局部ε（小量正参数）正则化方法，有效消除了退化现象对极点转移过程的不利影响.
   

关键词: 线性不等式组； 强迫性极点转移矩阵； 负旋转迭代； 局部ε正则化； , 定解问题

Abstract: With a view to more efficiently solving system of linear inequalities, a special matrix,  imposed basis-point transition matrix, was given together with  a special negative pivoting iteration operation, by which it can be better displayed that system of linear inequalities has both linear feature and geometric-plane feature. Moreover, based on the above platform, a new solution-decision method for system of linear inequalities was proposed. With the help of this new method, the solutiondecision process of system of linear inequalities can be changed into a series of elementary column transformations of matrixes. So, this method not only works fast and simply but also can be more easily translated into programs and more efficiently accomplished on computers. In addition, a simplex locally ε regularized method was proposed so as to overcome the bad effect coming from vertex degeneration, to the vertex transition iteration processes.

Key words: system of linear inequalities, imposed basis-point transition matrix, negative pivoting iteration, locally &epsilon, regularized; , solution-decision problem

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