Finding all solutions of piecewise-linear resistive circuits using the dual simplex method

Finding all solutions of piecewise-linear resistive circuits using the dual simplex method
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DOI：
10.1109/iscas.2000.858714
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发表时间：
2000-05
期刊：
2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353)
影响因子：
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通讯作者：
K. Yamamura;Shigeru Tanaka
K. Yamamura;Shigeru Tanaka
中科院分区：
其他
文献类型：
--
作者：
K. Yamamura;Shigeru Tanaka

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提出了一种利用线性规划(LP)求分段线性(PWL)阻性电路所有解的有效算法。这个算法是基于一个简单的检验(称为LP检验)来判断一组PWL方程在给定区域内不存在解。在LP测试中，将PWL方程组转化为LP问题，并应用单纯形法对其进行求解。这样的线性规划问题是通过用矩形包围PWL函数得到的。本文将对偶单纯形法引入到Lp检验中，使得每个区域的平均枢轴个数大大减少(例如少于1个)，从而使算法非常有效。
An efficient algorithm is proposed for finding all solutions of piecewise-linear (PWL) resistive circuits using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of PWL equations in a given region. In the LP test, the system of PWL equations is transformed in to an LP problem, to which the simplex method is applied. Such an LP problem is obtained by surrounding the PWL functions by rectangles. In this paper, we introduce the dual simplex method to the LP test, which makes the average number of pivotings per region much smaller (less than one, for example) and makes the algorithm very efficient.