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.

中文翻译：

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使用梯度方向获得牛顿型方法的全局收敛

在 Barzilai 和 Borwein [IMA Journal of Numerical Analysis, 8 (1988)] 的工作之后，对最速下降 (SD) 方法的重新关注促使我们考虑基于 SD 的全球化策略，该策略适用于任何线搜索方法. 特别是，我们将牛顿型方向与缩放的 SD 步长相结合，以获得合适的下降方向。就理论特征和计算行为而言，以合适的步长缩放 SD 方向与类似的全球化方法有显着差异。我们将我们的策略应用于 Newton 方法和 BFGS 方法，与为这些方法专门设计的完善的全球化策略的结果相比，计算结果看起来很有趣。