Spectral Scaling BFGS Method
Spectral Scaling BFGS Method
复制标题
光谱缩放 BFGS 方法
DOI：
10.1007/s10957-010-9652-y
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发表时间：
2010-08-01
影响因子：
1.9
通讯作者：
Li, D. H.
中科院分区：
文献类型：
--
作者：
Cheng, W. Y.;Li, D. H.
本文将拟牛顿方程尺度化，提出了一种谱尺度BFGS方法.该方法具有良好的自校正特性，可以改善BFGS方法的性能。与标准的BFGS方法相比，谱尺度BFGS方法在极小化n维二次函数时的单步收敛速度不会劣于最速下降法.此外，当应用精确线搜索方法极小化一个n维严格凸函数时，它在n步内终止。在适当的条件下，我们证明了谱尺度BFGS方法在Wolfe线搜索下对一致凸优化问题是全局收敛的，并且是R-线性收敛的。数值结果表明，谱标度BFGS方法优于标准BFGS方法。
In this paper, we scale the quasiNewton equation and propose a spectral scaling BFGS method. The method has a good selfcorrecting property and can improve the behavior of the BFGS method. Compared with the standard BFGS method, the single-step convergence rate of the spectral scaling BFGS method will not be inferior to that of the steepest descent method when minimizing an n-dimensional quadratic function. In addition, when the method with exact line search is applied to minimize an n-dimensional strictly convex function, it terminates within n steps. Under appropriate conditions, we show that the spectral scaling BFGS method with Wolfe line search is globally and R-linear convergent for uniformly convex optimization problems. The reported numerical results show that the spectral scaling BFGS method outperforms the standard BFGS method.