地点：行健楼学术活动室665
邀请人：孙海琳教授
In this talk, we consider the convergence behavior of Anderson acceleration algorithm for nonsmooth fixed point problems. First, 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. Second, we propose a smoothing approximation of the composite max function and show that the smoothing approximation for a class of contractive mappings is also a contraction mapping and has the same fixed point as the original problem, which confirms that the nonsmoothness can not affect the convergence properties of Anderson(m) algorithm when we use the proposed smoothing approximation instead of the original nonsmooth one. Third, we propose a novel Smoothing Anderson(m) algorithm by using a smoothing function of the original fixed point function and show its r-linear convergence. Furthermore, we prove the q-linear convergence of the Smoothing Anderson(1) algorithm. Finally, some numerical examples are given to demonstrate the efficiency of the proposed smoothing Anderson acceleration algorithms.
