@article{7f51f824eed3449787f22fa29fd2a440,
title = "Anderson acceleration for a class of nonsmooth fixed-point problems",
abstract = "We prove convergence of Anderson acceleration for a class of nonsmooth fixed-point problems for which the nonlinearities can be split into a smooth contractive part and a nonsmooth part which has a small Lipschitz constant. These problems arise from compositions of completely continuous integral operators and pointwise nonsmooth functions. We illustrate the results with two examples.",
keywords = "Anderson acceleration, Fixed-point problems, Integral equations, Nonlinear equations, Nonsmooth equatioins",
author = "Wei Bian and Xiaojun Chen and Kelley, {C. T.}",
note = "Funding Information: \ast Received by the editors April 6, 2020; accepted for publication (in revised form) November 23, 2020; published electronically January 20, 2021. https://doi.org/10.1137/20M132938X \bfF \bfu \bfn \bfd \bfi \bfn \bfg : This work of the first author was partially supported by the NSF foundation of China through grants 11871178 and 61773136. The work of the second author was partially supported by Hong Kong Research Grant Council grant 15300219. The work of the third author was partially supported by Army Research Office grant W911NF-16-1-0504 and National Science Foundation grants OAC-1740309, DMS-1745654, and DMS-1906446. \dagger School of Mathematics and Institute of Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, China (bianweilvse520@163.com). \ddagger Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China (maxjchen@polyu.edu.hk). \S Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205 USA (tim kelley@ncsu.edu). Publisher Copyright: {\textcopyright} 2020 Society for Industrial and Applied Mathematics Publications. All rights reserved.",
year = "2021",
month = jan,
day = "20",
doi = "10.1137/20M132938X",
language = "English",
volume = "0",
pages = "S1--S20",
journal = "SIAM Journal on Scientific Computing",
issn = "1064-8275",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "0",
}