| 线性不等式组的简单对偶非线性方法 |
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| 引用本文： | 陈士俊,孙永广,吴宗鑫,顾阿伦.线性不等式组的简单对偶非线性方法[J].运筹与管理,2001,10(3):44-50. |
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| 作者姓名： | 陈士俊 孙永广 吴宗鑫 顾阿伦 |
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| 作者单位： | 清华大学,核能技术研究院系统工程室,北京,100084 |
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| 摘 要： | 将线性不等式组问题转化为一个形式简单的对偶空间非线性极值问题，本提出了一类新的求解线性不等式组的方法-简单对偶非线性方法，它在理论上是多项式算法，并可以从任意点启动，可以应用共轭梯度方法有效地求解大规模线性不等式组问题。本给出了不同的算法实现，数值实验结果表明，简单对偶非线性方法是有效的。
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| 关 键 词： | 线性不等式组 简单对偶非线性方法 多项式算法 |
| 文章编号： | 1007-3221(2001)03-0044-07 |
| 修稿时间： | 2001年4月5日 |
A Class of Simple Dual Nonlinear Methods for Solving Linear Inequalities |
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| CHEN Shi-jun,SUN Yong-guang,WU Zong-xin,GU A-lun.A Class of Simple Dual Nonlinear Methods for Solving Linear Inequalities[J].Operations Research and Management Science,2001,10(3):44-50. |
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| Authors: | CHEN Shi-jun SUN Yong-guang WU Zong-xin GU A-lun |
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| Abstract: | This paper gives a class of simple dual nonlinear methods (SDNM)for solving linear inequalities,which completes by solving the nonlinear extremum of simple form on the dual space transferred from the primal problem of linear inequalities.SDNM is a polynomial time algorithm with the Newton's method, so that SDNM can solve large-scale linear inequalities.The implementation of SDNM is also discussed as well as the numerical tests. |
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| Keywords: | linear inequalities simple dual nonlinear method polynomial time algorithm |
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