Remarks on the updated Hessian matrix methods
Remarks on the updated Hessian matrix methods
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DOI：
10.1002/qua.10709
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发表时间：
2003-09-20
影响因子：
2.2
通讯作者：
Bofill, JM
中科院分区：
文献类型：
--
作者：
Bofill, JM
使用拟牛顿-拉夫森方法优化关于一组变量的函数意味着在每次迭代时更新海森矩阵。Broyden-Fletcher-Goldfarb-Shanno更新公式用于最小化，Murtagh-Sargent-Powell更新公式用于优化一阶鞍点。提出了两个新的Hessian矩阵更新公式。其中一个公式是使用指数权重导出的，应该用来定位一阶鞍点。第二个公式是TS-Broyden-Fletcher-Goldfarb-Shanno更新的一个修改，可用于最小和一阶鞍点优化。这两个更新的海森矩阵公式的性能是相同的，在许多情况下更好的Broyden-Fletcher-Goldfarb-Shanno和Murtagh-Sargent-Powell公式。(C)2003 Wiley Periodicals，Inc.
Optimizing a function with respect to a set of variables using the quasi-Newton-Raphson method implies updating the Hessian matrix at each iteration. The Broyden-Fletcher-Goldfarb-Shanno update formula is used for minimization and the Murtagh-Sargent-Powell update formula for optimization of first-order saddle points. Two new formulae are proposed to update the Hessian matrix. One of these formulae is derived using exponential weights and should be used to locate first-order saddle points. The second formula is a modification of the TS-Broyden-Fletcher-Goldfarb-Shanno update and could used for both minimum and first-order saddle point optimizations. These two update Hessian matrix formulae present a performance that is the same and in many cases better that the Broyden-Fletcher-Goldfarb-Shanno and Murtagh-Sargent-Powell formulae. (C) 2003 Wiley Periodicals, Inc.