| 带新的非线性互补函数的广义非精确牛顿法 |
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| 引用本文： | 濮定国,薛文娟,沈春根.带新的非线性互补函数的广义非精确牛顿法[J].同济大学学报(自然科学版),2005,33(8):1109-1113. |
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| 作者姓名： | 濮定国 薛文娟 沈春根 |
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| 作者单位： | 同济大学,应用数学系,上海,200092 |
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| 基金项目： | 国家自然科学基金资助项目（10371089） |
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| 摘 要： | 提出了新的弱正则伪光滑非线性互补（NCP）函数，该函数具有良好的性质．在这个新的NCP函数基础上，求解一个目标函数和约束函数都是光滑的最优化问题．构造半光滑方程组，用来求解非线性约束最优化问题的KKT点，然后用新提出的广义非精确牛顿法解这个半光滑方程组．该方法是可实现的，且具有全局收敛性．最后还证明了在较弱假设条件下，它具有局部超线性收敛性．
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| 关 键 词： | 约束非线性规划 半光滑 非线性互补 收敛性 |
| 文章编号： | 0253-374X（2005）08-1109-05 |
| 收稿时间： | 12 29 2003 12:00AM |
| 修稿时间： | 2003-12-29 |
Inexact Generalized Newton Method with New NCP Function |
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| PU Ding-guo,XUE Wen-juan,SHEN Chun-gen.Inexact Generalized Newton Method with New NCP Function[J].Journal of Tongji University(Natural Science),2005,33(8):1109-1113. |
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| Authors: | PU Ding-guo XUE Wen-juan SHEN Chun-gen |
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| Abstract: | In this paper,we present a new nonlinear complementarity (NCP) function which is piecewise linear-rational,regular pseudo-smooth and has nice properties.Then we apply the NCP function to some nonlinear optimization methods.We reformulate the problem for finding KKT points of the nonlinear constrained optimization problem as a system of semismooth equations by using the new NCP function.Then we consider the local behavior of inexact generalized Newton methods to solve the semismooth equations.The method is implementable and globally convergent.We also prove that the algorithm has superlinear convergence rates under some mild conditions. |
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| Keywords: | constrained nonlinear programming semismooth nonlinear complementarity convergence |
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