Abstract

In this paper, we introduce a novel dual variable algorithm accelerated via inertial extrapolation for solving the generalized split inverse problem given as a task of finding the common null point equality of finite family of inverse-strongly monotone mappings in Hilbert spaces. The proposed method uses the dual variable and self-adaptive technique, along with an inertial strategy which aims at getting accelerated convergence. We establish the convergence Theorem of the proposed method under some suitable assumptions. We also apply our result to solve several types of problems. Our results improve and generalize the corresponding several known results announced by many others. Numerical experiments are presented to show the efficiency and comparative performance of the proposed algorithm.

摘要

在本文中，我们引入了一种通过惯性外推加速的新型双变量算法，用于解决广义分裂逆问题，该问题作为在希尔伯特空间中寻找有限逆强单调映射族的公共零点等式的任务。所提出的方法使用双变量和自适应技术，以及旨在加速收敛的惯性策略。我们在一些合适的假设下建立了所提出方法的收敛定理。我们还将我们的结果应用于解决几种类型的问题。我们的结果改进并概括了许多其他人宣布的相应的几个已知结果。数值实验显示了所提出算法的效率和比较性能。