| 一类新的Lagrangian乘子法 |
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| 引用本文： | 李康弟,濮定国. 一类新的Lagrangian乘子法[J]. 运筹学学报, 2006, 10(4): 9-22 |
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| 作者姓名： | 李康弟 濮定国 |
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| 作者单位： | 1. 上海电力学院数理系,上海,200090
2. 同济大学应用数学系,上海,200092 |
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| 基金项目： | This research is supported by the National Science Foundation of China (No. 10571137) and the Natural Science Foundation of Shanghai Educational Committee(No.05LZ05) |
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| 摘 要： | 本文提出了求解光滑不等式约束最优化问题新的乘子法,在增广Lagrangian函数中,使用了新的NCP函数的乘子法．该方法在增广Lagrangian函数和原问题之间存在很好的等价性;同时该方法具有全局收敛性,且在适当假设下,具有超线性收敛率．本文给出了一个有效选择参数C的方法．
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| 关 键 词： | 运筹学 约束最优化 KKT点 乘子 NCP函数 收敛性 |
| 收稿时间： | 2004-08-23 |
| 修稿时间： | 2004-08-23 |
A Class of New Lagrangian Multiplier Methods |
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| Li Kangdi,Pu Dingguo. A Class of New Lagrangian Multiplier Methods[J]. OR Transactions, 2006, 10(4): 9-22 |
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| Authors: | Li Kangdi Pu Dingguo |
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| Abstract: | In this paper, a new class of augmented Lagrangian functions with the Fischer-Burmeister NCP function is proposed for the minimization of a smooth function subject to smooth equation and inequality constraints. We prove the equivalence between the unconstrained optimization and the primal constrained problem. This method is implementable and globally convergent. We also prove that the method has superlinear convergence rate under some mild conditions. In particular, we construct a function to adjust the parameter in the augmented Lagrangian function. |
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| Keywords: | Operation research constrained optimization KKT point multiplier nonlinear complementarity function convergence |
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