| 关于 Rosen 算法的注记 |
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| 引用本文： | 刘自成.关于 Rosen 算法的注记[J].系统科学与数学,1992,12(1):094-096. |
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| 作者姓名： | 刘自成 |
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| 作者单位： | 中国科学院应用数学研究所 北京100080
(刘自成，胡晓东，堵丁柱)，中国科学院应用数学研究所 北京100080(陈礴) |
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| 摘 要： | 1960年,Rosen 提出一个求线性不等式组可行解的投影算法.1981年,Powell给出一个例子说明 Rosen 的算法会发生循环从而失效.本文证明,按照 Rosen 的算法,只要适当地做点修正,循环就可避免,从而算法必在有限步内找到解或发现无解.首先给出一些记号.所考虑的问题是求 n 维向量 x 满足
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A NOTE ON ROSEN'S ALGORITHM |
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| Institution: | (1)Institute of Applied Mathematics,Academia Sinica,Beijing 100080;(2)Institute of Applied Mathematics,Academia Sinica,Beijing 100080;(3)Institute of Applied Mathematics,Academia Sinica,Beijing 100080;(4)Institute of Applied Mathematics,Academia Sinica,Beijing 100080 |
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| Abstract: | In 1960,Rosen gave an algorithm for finding a feasible solution to a given system of linearinequalities.In 1981,Powell gave an example showing that Rosen's algorithm may cycle in-stead of converge.in this paper,it is shown that a slight improvement on Rosen's algorithmcan avoid cycling.Thus,the improved algorithm must terminate in finitely many computa-tional steps either finding a feasible solution or concluding that there is no feasible solution. |
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