Paper Info
Title
Anderson Acceleration for Nonsmooth Fixed Point Problems
Abstract
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.
Year
DOI
Venue
2022
10.1137/22M1475983
SIAM J. Numer. Anal.
DocType
Volume
ISSN
Journal
60
SIAM Journal on Numerical Analysis (2022)
Citations 
PageRank 
References 
0
0.34
0
Authors
2
Name
Order
Citations
PageRank
Wei Bian128614.65
Xiaojun Chen21298107.51