ABSTRACT

In this paper, we study the so-called generalized monotone quasi-inclusion problem which is a generalization and extension of well-known monotone quasi-inclusion problem. We propose a forward–backward splitting method for solving this problem in the framework of reflexive Banach spaces. Based on Bregman distance function, we prove a strong convergence result of the proposed algorithm to a common zero of the problem. As an application, we apply the main result to the variational inequality problem. Finally, we provide some numerical examples to demonstrate our algorithm performance. The results presented in this paper improve and extend many known results in the literature.

摘要

在本文中，我们研究了所谓的广义单调准包含问题，它是众所周知的单调准包含问题的推广和扩展。我们提出了一种在自反巴拿赫空间框架内解决这个问题的前向-后向分裂方法。基于 Bregman 距离函数，我们证明了所提出的算法对问题的公共零点的强收敛结果。作为应用，我们将主要结果应用于变分不等式问题。最后，我们提供了一些数值例子来展示我们的算法性能。本文提出的结果改进并扩展了文献中的许多已知结果。