A NEW PROJECTION METHOD FOR SOLVING THE SPLIT VARIATIONAL INEQUALITY PROBLEM IN HILBERT SPACES

Authors

  • Thang Truong Dang Hanoi University of Science and Technology

Keywords:

Split variational inequality problem, Split feasibility problem, Hillbert spaces, Metric projection

Abstract

This paper proposes a new algorithm for solving the split variational inequality problem in Hilbert spaces. In order to solve this problem, we propose a new algorithm and establish a strong convergence theorem for it. Compared with the work by Censor et al. (Numer. Algor., 59:301-323, 2012), the new algorithm gives strong convergence results. It shows that the iterative method converges strongly under weaker assumptions than the ones used recently. Some numerical examples are also given to illustrate the convergence analysis of the considered method.

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References

[1] Y. Censor, A. Gibali and S. Reich, Algorithms for the split variational inequality problem, Numer. Algorithms, 59 (2012), 301–323.

[2] Moudafi, A.: Viscosity approximation methods for fixed–points problems. J. Math. Anal. Appl., 241, 46–55 (2000)

[3] C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Probl., 18 (2002), 441–453.

[4] Bauschke HH, Combettes PL. Convex analysis and monotone operator theory in Hilbert spaces. New York: Springer. 2011.

[5] Chidume CE. Geometric properties of Banach spaces and nonlinear iterations. Springer VerlagSeries,LectureNotesinMathematics,ISBN 978-1-84882-189-7. 2009.

[6] Goebel K, Kirk WA. Topics in Metric Fixed Point Theory. Cambridge Stud Adv Math. 28. Cambridge: Cambridge University Press. 1990.

[7] Maingé PE. Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization. Set-Valued Anal. 2008;16:899–912.

[8] Xu HK. Strong convergence of an iterative method for nonexpansive and accretive operators. J Math Anal Appl. 2006;314(2):631–643.

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Published

2023-06-27

How to Cite

Truong Dang, T. (2023). A NEW PROJECTION METHOD FOR SOLVING THE SPLIT VARIATIONAL INEQUALITY PROBLEM IN HILBERT SPACES. SCIENTIFIC JOURNAL OF TAN TRAO UNIVERSITY, 9(3). Retrieved from https://tckh.daihoctantrao.edu.vn/index.php/sjttu/article/view/950

Issue

Vol. 9 No. 3 (2023): Natural Science - Engineering - Technology

Section

Natural Science and Technology

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