| 解约束优化的分段线性有理NCP函数 |
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| 引用本文： | 濮定国,沈春根,薛文娟.解约束优化的分段线性有理NCP函数[J].应用数学与计算数学学报,2005,19(1):19-24. |
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| 作者姓名： | 濮定国 沈春根 薛文娟 |
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| 作者单位： | 同济大学应用数学系,上海,200000 |
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| 基金项目： | 国家自然科学基金项目No．10371899资助． |
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| 摘 要： | 本文给出新的NCP函数,这些函数是分段线性有理正则伪光滑的,且具有良好的性质.把这些NCP函数应用到解非线性优化问题的方法中.例如,把求解非线性约束优化问题的KKT点问题分别用QP-free方法,乘子法转化为解半光滑方程组或无约束优化问题.然后再考虑用非精确牛顿法或者拟牛顿法来解决该半光滑方程组或无约束优化问题.这个方法是可实现的,且具有全局收敛性.可以证明在一定假设条件下,该算法具有局部超线性收敛性.
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| 关 键 词： | 约束优化 半光滑 非线性互补 收敛性 |
| 修稿时间： | 2004年6月17日 |
Piecewise Linear-Rational NCP Function for Constrained Optimization |
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| PU Dingguo,Shen Chungen,Xue Wenjuan.Piecewise Linear-Rational NCP Function for Constrained Optimization[J].Communication on Applied Mathematics and Computation,2005,19(1):19-24. |
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| Authors: | PU Dingguo Shen Chungen Xue Wenjuan |
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| Institution: | Pu Dingguo Shen Chungen Xue Wenjuan Department of Mathematics,Tongji University,Shanghai 200092 |
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| Abstract: | In this paper, we present some new NCP functions which are piecewise linear-rational, regular pseudo-smooth and have nice properties. Then we apply these NCP functions 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 QP-free methods and Lagrangian Multiplier Methods. Then we consider the local behavior of inexact generalized Newton methods or quasi-Newton methods to solve the semismooth equations. |
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| Keywords: | constrained optimization semismooth nonlinear complementarity convergence |
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