| 非线性不等式组的光滑近似方法及其收敛性 |
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| 引用本文： | 何郁波,林晓艳,董晓亮.非线性不等式组的光滑近似方法及其收敛性[J].应用数学学报,2011,34(4). |
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| 作者姓名： | 何郁波 林晓艳 董晓亮 |
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| 作者单位： | 1. 怀化学院数学系,怀化,418008
2. 北方民族大学信息与计算科学学院,银川,750021 |
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| 基金项目： | 湖南省自然科学基金(06JJ5013); 湖南省教育厅重点(08A503); 宁夏高等学校科学研究(2009JY006); 北方民族大学自主科研项目青年(2011ZQY025)资助项目 |
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| 摘 要： | 将非线性不等式组的求解转化成非线性最小二乘问题,利用引入的光滑辅助函数,构造新的极小化问题来逐次逼近最小二乘问题.在一定的条件下,文中所提出的光滑高斯-牛顿算法的全局收敛性得到保证.适当条件下,算法的局部二阶收敛性得到了证明.文后的数值试验表明本文算法有效.
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| 关 键 词： | 非线性不等式组 光滑高斯-牛顿法 逐次近似 全局收敛 |
On the Convergence of Smoothing Approximate Method for Nonlinear Inequalities |
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| HE YUBO,LIN XIAOYAN,DONG XIAOLIANG.On the Convergence of Smoothing Approximate Method for Nonlinear Inequalities[J].Acta Mathematicae Applicatae Sinica,2011,34(4). |
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| Authors: | HE YUBO LIN XIAOYAN DONG XIAOLIANG |
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| Institution: | HE YUBO~ LIN XIAOYAN (Department of Mathematics,Huaihua University,Huaihua 418008) DONG XIAOLIANG (School of Information and Computation Science,the North University for Ethnics,Yinchuan 750021) |
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| Abstract: | Consider nonlinear inequalities,we reformulate nonlinear inequalities as nonlinear least squares problems.Using smoothing function,we construct a new optimization to approximate the least squares problems.Under some conditions,the convergence of our algorithm is proved and we analysis local quadratic rate.Numerical examples are given to illustrate our method. |
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| Keywords: | nonlinear inequalities smoothing Gauss-Newton method successive approximate global convergent |
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