一种求解包含问题的算法研究

An Algorithm for Solving Inclusion Problems

一种实希尔伯特空间中求解包含问题的算法被提出,所提出的算法基于向前向后方法、压缩方法、惯性方法和无需搜索的自适应步长。算法的特点为迭代中多次使用惯性加速方法,且自适应步长随着迭代次数增加可能增大。在包含问题解集非空、一个映射极大单调、另一个映射单调且利普希茨连续的假设下,算法的强收敛性被证明。

In this work,a new method for solving inclusion problems in real Hilbert space is given.The algorithm is inspired by forward-backward splitting method,contraction method,inertial method and self-adaptive step sizes.The characteristic of the algorithm is that the inertial acceleration method is used many times in the iteration,and the adaptive step size may increase with the increase of the number of iterations.Under the assumption that the solution set of the inclusion problem is non-empty,one map is maximally monotone,and the other map is monotone and Lipschitz continuous,the strong convergence of the algorithm is proved.