Acta Mathematica Vietnamica

, Volume 42, Issue 4, pp 587–604

# An Extragradient Method for Finding Minimum-Norm Solution of the Split Equilibrium Problem

• Tran Viet Anh
Article

## Abstract

The purpose of this paper is to find minimum-norm solutions of the split equilibrium problem. This problem is motivated by the least-squares solution to the constrained linear inverse problem. By using the extragradient method, we derive the strong convergence of an iterative algorithm to the minimum-norm solution of the split equilibrium problem. As special cases, minimum-norm solutions of the split variational inequality problem and the split feasibility problem can be found.

## Keywords

Split equilibrium problem Minimum-norm solution Strong convergence

## Mathematics Subject Classification (2010)

49M37 90C26 65K15

## Notes

### Acknowledgments

The author is very grateful to the anonymous referee and the editor for their useful comments and advices which helped to improve the quality and presentation of this paper.

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