论文标题
非线性Schwarz的准牛顿方法的预处理
Nonlinear Schwarz preconditioning for Quasi-Newton methods
论文作者
论文摘要
我们提出了非线性限制的添加剂Schwarz（RAS）预处理策略，以提高有限存储器准Newton（QN）方法的收敛速度。我们认为“左侧的”和“右键”策略。随着非线性预处理的应用将标准梯度和黑森人更改为其预处理的对应物，标准的SECANT对不能用于近似预处理的Hessians。我们讨论了如何在预处理的QN框架中构造割线对。最后，我们使用数值实验证明了预处理方法的鲁棒性和效率。
We propose the nonlinear restricted additive Schwarz (RAS) preconditioning strategy to improve the convergence speed of limited memory quasi-Newton (QN) methods. We consider both "left-preconditioning" and "right-preconditioning" strategies. As the application of the nonlinear preconditioning changes the standard gradients and Hessians to their preconditioned counterparts, the standard secant pairs cannot be used to approximate the preconditioned Hessians. We discuss how to construct the secant pairs in the preconditioned QN framework. Finally, we demonstrate the robustness and efficiency of the preconditioned QN methods using numerical experiments.
