A NEW APPROACH TO VARIABLE METRIC ALGORITHMS
A NEW APPROACH TO VARIABLE METRIC ALGORITHMS
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DOI：
10.1093/comjnl/13.3.317
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发表时间：
1970-01-01
期刊：
影响因子：
1.4
通讯作者：
FLETCHER, R
中科院分区：
文献类型：
--
作者：
FLETCHER, R
变尺度算法的一种方法已被研究，其中线性搜索子问题不再成为必要的。二次终止的性质已被取代的逼近矩阵的特征值的逆海森单调收敛之一。建立了一个具有这种性质的更新公式的凸类，并指出了一种选择该类成员的策略，以使逼近远离奇异性和无界性。一个FORTRAN程序已被广泛测试，令人鼓舞的结果。
An approach to variable metric algorithms has been investigated in which the linear search sub-problem no longer becomes necessary. The property of quadratic termination has been replaced by one of monotonic convergence of the eigenvalues of the approximating matrix to the inverse hessian. A convex class of updating formulae which possess this property has been established, and a strategy has been indicated for choosing a member of the class so as to keep the approximation away from both singularity and unboundedness. A FORTRAN program has been tested extensively with encouraging results.