A Relaxed Tseng's Method-based Algorithm for Solving Split Variational Inequalities with Multiple Output Sets

• Published in: Numerical functional analysis and optimization Vol. 45; no. 15; pp. 733 - 758
• Main Authors: Tong, Xiaolei, Ling, Tong, Shi, Luoyi
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 17.11.2024; Taylor & Francis Ltd
• Subjects: Adaptive algorithms; Banach space; Banach spaces; Convergence; multiple-sets split variational inequalities; non-Lipschitz operators; Operators (mathematics); pseudomonotone operators; Tsengs extragradient method
• ISSN: 0163-0563; 1532-2467
• DOI: 10.1080/01630563.2024.2405482

In this paper, the split variational inequality problem with multiple output sets is considered in a more general framework of reflexive Banach spaces. We introduce a relaxed Tseng extragradient method for approximating the solution of this problem when the cost operators are pseudomonotone and non-Lipschitz. Moreover, our proposed algorithm employs the inertial technique and a new self-adaptive step size to guarantee high rate of convergence. Strong convergence of the algorithm is proved in this case without the need for the sequential weak continuity condition. Finally, some numerical experiments are given to show the applicability of our proposed algorithm.