| 非线性优化修正Frisch函数方法的乘子映射 |
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| 引用本文： | 孔德宝,张立卫.非线性优化修正Frisch函数方法的乘子映射[J].运筹学学报,2009,13(3). |
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| 作者姓名： | 孔德宝 张立卫 |
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| 作者单位： | 1. 呼伦贝尔学院数学系,海拉尔,021008
2. 大连理工大学数学科学学院,大连,116024 |
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| 摘 要： | 对于同时含有等式与不等式约束的非线性优化问题的修正Frisch函数方法,给出其乘子映射和解映射的导数的估计.将得到的估计用于建立修正Frisch函数方法的线性收敛速率.在线性无关的约束规范,严格互补条件和二阶充分性条件成立的前提下,证得该收敛率与1/c成正比.本文的收敛性分析依赖于矩阵的奇异值分解,其方法可以用来分析其他的修正Lagrange方法.
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| 关 键 词： | 运筹学 修正Frisch函数方法 非线性优化 乘子映射 收敛率 |
On the Multiplier Mapping of the Modified Frisch Function Method for Nonlinear Optimization |
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| Kong Debao,Zhang Liwei.On the Multiplier Mapping of the Modified Frisch Function Method for Nonlinear Optimization[J].OR Transactions,2009,13(3). |
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| Authors: | Kong Debao Zhang Liwei |
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| Abstract: | We estimate the derivatives of the multiplier mapping and the solution mapping of the modified Frisch function method for nonlinear optimization problems with both equality and inequality constraints. The estimates are used to establish the linear rate of convergence of the the modified Frisch function method, which is proportional to 1/c with the penalty parameter c exceeding a threshold c>0, under the linear indepen-dence constraint qualification, the strict complementarity condition and the second order sufficient condition. The analysis is based on the singular value decompositions of matri-ces and the methodology in this paper can be used to analyze other modified Lagrange methods. |
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| Keywords: | Operations research the modified Frisch function method nonlinear optimization multiplier mapping rate of convergence |
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