PreprintArticleVersion 1Preserved in Portico This version is not peer-reviewed
Novel Accelerated Cyclic Iterative Approximation for Hierarchical Variational Inequalities Constrained by Multiple-Set Split Common Fixed Point Problems
Version 1
: Received: 27 August 2024 / Approved: 4 September 2024 / Online: 5 September 2024 (02:31:57 CEST)
How to cite:
Ye, Y.; Lan, H. Novel Accelerated Cyclic Iterative Approximation for Hierarchical Variational Inequalities Constrained by Multiple-Set Split Common Fixed Point Problems. Preprints2024, 2024090352. https://doi.org/10.20944/preprints202409.0352.v1
Ye, Y.; Lan, H. Novel Accelerated Cyclic Iterative Approximation for Hierarchical Variational Inequalities Constrained by Multiple-Set Split Common Fixed Point Problems. Preprints 2024, 2024090352. https://doi.org/10.20944/preprints202409.0352.v1
Ye, Y.; Lan, H. Novel Accelerated Cyclic Iterative Approximation for Hierarchical Variational Inequalities Constrained by Multiple-Set Split Common Fixed Point Problems. Preprints2024, 2024090352. https://doi.org/10.20944/preprints202409.0352.v1
APA Style
Ye, Y., & Lan, H. (2024). Novel Accelerated Cyclic Iterative Approximation for Hierarchical Variational Inequalities Constrained by Multiple-Set Split Common Fixed Point Problems. Preprints. https://doi.org/10.20944/preprints202409.0352.v1
Chicago/Turabian Style
Ye, Y. and Hengyou Lan. 2024 "Novel Accelerated Cyclic Iterative Approximation for Hierarchical Variational Inequalities Constrained by Multiple-Set Split Common Fixed Point Problems" Preprints. https://doi.org/10.20944/preprints202409.0352.v1
Abstract
In this paper, we investigate a class of hierarchical variational inequalities (HVIPs, i.e., strongly monotone variational inequality problems defined on the solution set of multiple-set split common fixed point problems) with quasi-pseudocontractive mappings in real Hilbert spaces, which special cases can be found in many important engineering practical applications such as image recognizing, signal processing and machine learning. In order to solve HVIPs of potential application value, inspired by the primal-dual algorithm, we propose a novel accelerated cyclic iterative algorithm that combines the inertial method with a correction term and a self-adaptive step-size technique. Our approach eliminates the need for prior knowledge of the bounded linear operator norm. Under appropriate assumptions, we establish strong convergence of the algorithm. Finally, we apply our novel iterative approximation to solve multiple-set split feasibility problems and verify the effectiveness of the proposed iterative algorithm through numerical results.
Computer Science and Mathematics, Computational Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
