标题： 两步惯性Bregman交替结构自适应邻近梯度下降算法用于非凸和非光滑问题 显示英文标题

标题： Two-step inertial Bregman alternating structure-adapted proximal gradient descent algorithm for nonconvex and nonsmooth problems

摘要： 在本文中，我们引入了几种加速迭代算法，用于求解实希尔伯特空间中拟非扩张算子的多集分裂公共固定点问题。 基于原始对偶方法，我们以结合惯性技术和自适应步长的方式构造了几种迭代算法，使得算法的实现不需要任何关于有界线性算子范数的先验信息。 在适当的假设下，建立了所提出算法的弱收敛性。 作为应用，我们得到了相对的迭代算法来解决多集分裂可行性问题。 最后，通过数值实验说明了所提出算法的性能。 显示英文摘要

摘要： In the paper, we introduce several accelerate iterative algorithms for solving the multiple-set split common fixed-point problem of quasi-nonexpansive operators in real Hilbert space. Based on primal-dual method, we construct several iterative algorithms in a way that combines inertial technology and the self-adaptive stepsize such that the implementation of the algorithms doesn't need any prior information about bounded linear operator norm. Under suitable assumptions, weak convergence of the proposed algorithms is established. As applications, we obtain relative iterative algorithms to solve the multiple-set split feasibility problem. Finally, the performance of the proposed algorithms is illustrated by numerical experiments.