| 寻找非线性规划问题Kuhn-Tucker 点的一种微分方程方法 |
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| 引用本文： | 周丽美,张立卫. 寻找非线性规划问题Kuhn-Tucker 点的一种微分方程方法[J]. 大连理工大学学报, 2005, 45(6): 920-924 |
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| 作者姓名： | 周丽美 张立卫 |
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| 作者单位： | 大连理工大学,应用数学系,辽宁,大连,116024;青岛理工大学,理学院,山东,青岛,266033;大连理工大学,应用数学系,辽宁,大连,116024 |
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| 摘 要： | 为了寻找带有等式约束和不等式约束的非线性规划问题的Kuhn-Tucker点,给出了一种微分方程系统.在一定的条件下,证明了非线性规划问题的Kuhn-Tucker点是微分方程系统的渐进稳定平衡点,并且基于一般微分方程系统的数值积分建立了一个数值算法,然后给出了该数值算法的收敛性定理.数值算例表明了该算法的有效性.
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| 关 键 词： | 非线性规划 微分方程 平衡点 稳定 |
| 文章编号： | 1000-8608（2005）06-0920-05 |
| 收稿时间： | 2004-08-19 |
| 修稿时间： | 2004-08-192005-10-08 |
A differential equation approach to finding a Kuhn-Tucker point of a nonlinear programming problem |
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| ZHOU Li-mei,ZHANG Li-wei. A differential equation approach to finding a Kuhn-Tucker point of a nonlinear programming problem[J]. Journal of Dalian University of Technology, 2005, 45(6): 920-924 |
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| Authors: | ZHOU Li-mei ZHANG Li-wei |
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| Affiliation: | 1. Dept. of Appl. Math., Dalian Univ. of Technol., Dalian 116024, China; 2. College of Sci., Qingdao Technol. Univ., Qingdao 266033, China |
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| Abstract: | A system of differential equations is constructed to find Kuhn-Tucker points of a nonlinear programming problem with both equality and inequality constraints.It is proved that the Kuhn-Tucker point of the nonlinear programming problem is an asymptotically stable equilibrium point of the differential system and a numerical algorithm is given based on the numerical integration of the proposed system of ordinary differential equations.The convergence theorem of the numerical algorithm is demonstrated.Several illustrative examples show the effectiveness of the algorithm. |
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| Keywords: | nonlinear programming differential equation equilibrium solution stable |
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