| 非线性约束优化问题的一个修正 Lagrangian 算法 |
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| 引用本文： | 贺素香,张立卫.非线性约束优化问题的一个修正 Lagrangian 算法[J].数学物理学报(A辑),2006,26(1):49-062. |
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| 作者姓名： | 贺素香 张立卫 |
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| 作者单位： | 武汉理工大学理学院，大连理工大学应用数学系 武汉 430070，大连 116024 |
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| 基金项目： | 国家青年自然科学基金(10001007)，武汉理工大学博士科研基金资助 |
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| 摘 要： | 基于一个含有控制参数的修正Lagrangian函数,该文建立了一个求解非线性约束优化问题的修正Lagrangian算法.在一些适当的条件下,证明了控制参数存在一个阀值,当控制参数小于这一阀值时,由这一算法产生的序列解局部收敛于问题的Kuhn-Tucker点,并且建立了解的误差上界.最后给出一些约束优化问题的数值结果.
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| 关 键 词： | 修正Lagrangian算法 非线性约束优化问题 局部收敛 误差界 |
| 文章编号： | 1003-3998(2006)01-049-14 |
| 收稿时间： | 2003-09-25 |
| 修稿时间： | 2005-04-05 |
A Modified Lagrangian Algorithm for Solving Nonlinear Constrained Optimization Problems |
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| He Suxiang,Zhang Liwei.A Modified Lagrangian Algorithm for Solving Nonlinear Constrained Optimization Problems[J].Acta Mathematica Scientia,2006,26(1):49-062. |
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| Authors: | He Suxiang Zhang Liwei |
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| Institution: | 1.School of Science, Wuhan University of Technology, Wuhan 430070; 2. Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 |
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| Abstract: | A modified Lagrangian algorithm for solving nonlinear constrained optimization problems is established, which is based on a modified Lagrange function with a controlling parameter. Under suitable conditions, the local convergence of the modified Lagrangian algorithm is proved and the error bounds of solutions are established, which shows that there exists a threshold of the parameter such that, when the parameter is less than this threshold, the sequence of points generated by the algorithm converges to a Kuhn-Tucker point locally. Numerical results by using the modified Lagrangian algorithm for solving some simple constrained optimization problems are illustrated. |
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| Keywords: | Modified Lagrangian algorithm Nonlinear constrained optimization problems Local convergence Error bound |
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