| 非负线性最小二乘问题的一种严格可行内点算法 |
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| 引用本文： | 雍龙泉.非负线性最小二乘问题的一种严格可行内点算法[J].陕西工学院学报,2010(4):84-89,F0003. |
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| 作者姓名： | 雍龙泉 |
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| 作者单位： | 陕西理工学院数学系,陕西汉中723001 |
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| 基金项目： | 陕西省教育厅科研基金资助项目（09JK381） |
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| 摘 要： | 给出了非负线性最小二乘问题的一个新算法。首先,把非负线性最小二乘转化为线性互补问题,结合牛顿方向和中心路径方向,通过求解一个线性方程组得到搜索方向;进而获得了求解非负线性最小二乘问题的一种严格可行内点算法,并证明该算法经过多项式次迭代之后收敛到原问题的一个最优解,数值实验表明此方法是有效的。
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| 关 键 词： | 非负线性最小二乘问题 线性互补问题 可行内点算法 多项式复杂性 |
A new feasible interior point method to nonnegative linear least squares problems |
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| YONG Long-quan.A new feasible interior point method to nonnegative linear least squares problems[J].Journal of Shaanxi Institute of Technology,2010(4):84-89,F0003. |
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| Authors: | YONG Long-quan |
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| Affiliation: | YONG Long-quan (Department of Mathematical Sciences,Shaanxi University of Technology,Hanzhong 723001,China) |
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| Abstract: | A new method of solving nonnegative linear least squares problems was presented.Firstly,nonnegative linear least squares problem was transformed into linear complementarity problem.By combining Newton direction and centering direction,the search direction by solving a linear system was obtained.Then a feasible interior point algorithm for nonnegative linear least squares problem was established and the results showed that this method was polynomial in complexity.At last,some numerical examples to indicate that the method is feasible and effective were given. |
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| Keywords: | nonnegative linear least squares problem linear complementarity problem feasible interior point algorithm polynomial complexit |
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