论文标题
使用梯度方向获得牛顿型方法的全球收敛性
Using gradient directions to get global convergence of Newton-type methods
论文作者
论文摘要
Barzilai和Borwein的工作后，对最陡峭下降（SD）方法的新兴趣[IMA数字分析杂志，8（1988）]驱使我们考虑基于SD的全球化策略，该策略适用于任何线索搜索方法。特别是，我们将牛顿型方向与缩放的SD步骤相结合，以具有合适的下降方向。在理论特征和计算行为方面，用合适的步长缩放SD方向在相似的全球化方法方面具有显着差异。我们将我们的策略应用于牛顿的方法和BFGS方法，与确定的全球化策略的结果相比，计算结果似乎很有趣。
The renewed interest in Steepest Descent (SD) methods following the work of Barzilai and Borwein [IMA Journal of Numerical Analysis, 8 (1988)] has driven us to consider a globalization strategy based on SD, which is applicable to any line-search method. In particular, we combine Newton-type directions with scaled SD steps to have suitable descent directions. Scaling the SD directions with a suitable step length makes a significant difference with respect to similar globalization approaches, in terms of both theoretical features and computational behavior. We apply our strategy to Newton's method and the BFGS method, with computational results that appear interesting compared with the results of well-established globalization strategies devised ad hoc for those methods.
