New Quasi-Newton Equation and Related Methods for Unconstrained Optimization
New Quasi-Newton Equation and Related Methods for Unconstrained Optimization
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DOI：
10.1023/a:1021898630001
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发表时间：
1999-07
影响因子：
1.9
通讯作者：
Jingfeng Zhang;N. Deng;L. Chen
中科院分区：
文献类型：
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作者：
Jingfeng Zhang;N. Deng;L. Chen
在无约束优化中，通常的拟牛顿方程是Bk +1sk=yk，其中yk是最后两次迭代的梯度之差。本文提出了一个新的拟牛顿方程，它是基于最后两次迭代的函数值和梯度的。新方程比旧方程更好地逼近2 f（xk+1）skthanyk，在这个意义上，新方程优于旧方程上级。基于新拟牛顿方程的修正拟牛顿法具有局部收敛性和超线性收敛性。大量的数值实验表明，新的拟牛顿方法是令人鼓舞的。
In unconstrained optimization, the usual quasi-Newton equation isBk+1sk=yk, whereykis the difference of the gradients at the last two iterates. In this paper, we propose a new quasi-Newton equation,, in whichis based on both the function values and gradients at the last two iterates. The new equation is superior to the old equation in the sense thatbetter approximates ∇2f(xk+1)skthanyk. Modified quasi-Newton methods based on the new quasi-Newton equation are locally and superlinearly convergent. Extensive numerical experiments have been conducted which show that the new quasi-Newton methods are encouraging.