AN ITERATIVE ALGORITHM FOR FINDING THE MINIMUM NORM POINT IN THE SOLUTION SET OF SPLIT FIXED POINT PROBLEM

Nguyễn Trung Nghĩa; Nguyễn Tất Thắng

doi:10.34238/tnu-jst.4024

AN ITERATIVE ALGORITHM FOR FINDING THE MINIMUM NORM POINT IN THE SOLUTION SET OF SPLIT FIXED POINT PROBLEM

About this article

Received: 23/02/21 Revised: 18/05/21 Published: 26/05/21

Authors

1. Nguyen Trung Nghia, School of Applied Mathematics and Informatics, Hanoi University of Science and Technology
2. Nguyen Tat Thang , Thai Nguyen University

Abstract

The split feasibility problem and the variational inequality problem have many practical applications in signal processing, image reconstruction intensity-modulated radiation therapy, optimal control theory and many other fields. The problem we consider here is a bilevel problem, when the leader problem is the minimum norm point problem and the follower one is the split fixed point problem. The minimum norm point problem is a particular case of the variational inequality problem, when the cost mapping is the unit operator of the Hilbert space. In this paper, we propose an iterative method for approximating the solution of the bilevel problem. This method bases on the result presented by Tran Viet Anh and Le Dung Muu in 2016, which is a combination between the p ro jection method for variational inequality and the Krasnoselskii–Mann scheme for fixed points of nonexpansive mappings. The strong convergence of the method is proven. We close the paper by considering an example to illustrate the strong convergence of method.

Keywords

Split feasibility problem; Variational inequality; Hillbert spaces; Nonexpansive mapping; Fixed point

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DOI: https://doi.org/10.34238/tnu-jst.4024

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