论文标题
安德森（Anderson）加速非平滑固定点问题
Anderson Acceleration for Nonsmooth Fixed Point Problems
论文作者
论文摘要
我们为复合$ \ max $固定点问题提供了安德森加速度的新收敛结果。我们证明，与现有Q因子相比，Anderson（1）和Ediis（1）是Q线性收敛的，其Q因子较小。此外，我们提出了合成固定点问题中复合最大函数的平滑近似。我们证明平滑近似是一个收缩映射，其固定点与复合$ \ max $固定点问题相同。我们的结果严格地确认，当我们使用提出的平滑近似值$ \ Max Max $固定点问题时，非平滑度不影响Anderson加速方法的收敛速率。提出了受约束最小问题，互补性问题和非平滑微分方程的数值结果，以显示拟议的Anderson加速方法的效率和良好性能，并具有平滑的近似值。
We give new convergence results of Anderson acceleration for the composite $\max$ fixed point problem. We prove that Anderson(1) and EDIIS(1) are q-linear convergent with a smaller q-factor than existing q-factors. Moreover, we propose a smoothing approximation of the composite max function in the contractive fixed point problem. We show that the smoothing approximation is a contraction mapping with the same fixed point as the composite $\max$ fixed point problem. Our results rigorously confirm that the nonsmoothness does not affect the convergence rate of Anderson acceleration method when we use the proposed smoothing approximation for the composite $\max$ fixed point problem. Numerical results for constrained minimax problems, complementarity problems and nonsmooth differential equations are presented to show the efficiency and good performance of the proposed Anderson acceleration method with smoothing approximation.
