论文标题
梯度方法中的谐波框架
A harmonic framework for stepsize selection in gradient methods
论文作者
论文摘要
我们研究了与渐变方法中的渐变方法选择的反向谐波雷利特商的使用，以实现非线性不受约束的优化问题的梯度选择。这不仅提供了一个优雅而灵活的框架，可以参数化和重新解释现有的步骤大小方案，而且还为新的灵活且可调的渐变家庭提供了灵感。特别是，我们将自适应的Barzilai-Borwein方法分析并将其扩展到一个新的步骤。尽管该家族为目标利用负值，但我们也考虑了积极的目标。我们提出了Dai和Liao（2002）扩展结果的二次问题的收敛分析，并进行了概述方法潜力的实验。
We study the use of inverse harmonic Rayleigh quotients with target for the stepsize selection in gradient methods for nonlinear unconstrained optimization problems. This provides not only an elegant and flexible framework to parametrize and reinterpret existing stepsize schemes, but also gives inspiration for new flexible and tunable families of steplengths. In particular, we analyze and extend the adaptive Barzilai-Borwein method to a new family of stepsizes. While this family exploits negative values for the target, we also consider positive targets. We present a convergence analysis for quadratic problems extending results by Dai and Liao (2002), and carry out experiments outlining the potential of the approaches.
