惯性广义Mann-Halpern算法及其应用

Inertial Generalized Mann-Halpern Algorithm and Its Application

本文主要研究Hilbert空间中非扩张映射的不动点问题。提出了一种惯性广义Mann-Halpern算法。在一定条件下证明了算法的强收敛性。将算法应用于求解Fermat-Weber定位问题,并给出数值实验结果。相比较已有算法,该算法在参数的选取上更具灵活性。

We considered the fixed point problem of nonexpansive mapping in Hilbert space. We proposed an inertial generalized Mann-Halpern algorithm. Giving certain conditions, we proved the strong convergence of the algorithm. Then we applied the algorithm to solve the Fermat-Weber location problem, and gave a numerical experiment. Com- pared with algorithms had been proposed before, our algorithm has the flexibility on choosing parameters.