| 一种新的保护牛顿法 |
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| 引用本文： | 董名垂.一种新的保护牛顿法[J].清华大学学报(自然科学版),1984(4). |
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| 作者姓名： | 董名垂 |
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| 作者单位： | 自动化系 |
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| 摘 要： | 本文提出了解无约束非线性规划问题的一种新的保护牛顿法。该法的实质是寻优过程中在牛顿迭代法产生的每一序列点，把ＢＦＧＳ或ＤＦＰ法尺度矩阵的逆和一适当的标量相乘，然后加到在该点求得的原问题的Ｈｅｓｓｅ矩阵上，从而保证合成矩阵的正定性。再采用Ｃｈｏｌｅｓｋｙ分解得到下次迭代的搜索方向。按本途径所得的算法是一系列简单的算术运算。用此法求解八个标准非线性检验问题所得结果是令人满意的。本文示出了这些结果并与各种下降法进行了初步比较。
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| 关 键 词： | 无约束非线性规划问题 拟牛顿法 保护牛顿法 Cholesky分解 |
A New Approach for Safeguarding Newton Method |
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| Dong Mingchui.A New Approach for Safeguarding Newton Method[J].Journal of Tsinghua University(Science and Technology),1984(4). |
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| Authors: | Dong Mingchui |
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| Institution: | Department of Automation |
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| Abstract: | This paper proposes a new approach for safeguarding Newton method in solving unconstrained non-linear programming problems. By adding an inverse BFGS or DFP metric matrix with a proper scalar to Hessian matrix of the problem at each sequential point, the positive definity of matrices can be guaranteed and the search direction is obtained by using Cholesky's procedure. The simpli- city of its algorithm and competitive application to eight popular test problems as well as comparision with some other descent methods are shown. |
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| Keywords: | unconstrained non-linear programming problem Quasi-Newton method safeguarding Newton method Cholesky's factorization |
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