An Extragradient Method for Finding Minimum-Norm Solution of the Split Equilibrium Problem
- 168 Downloads
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.
KeywordsSplit equilibrium problem Minimum-norm solution Strong convergence
Mathematics Subject Classification (2010)49M37 90C26 65K15
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.
- 11.Censor, Y., Segal, A.: Iterative projection methods in biomedical inverse problems. In: Censor, Y, Jiang, M., Louis, A.K. (eds.) Mathematical Methods in Biomedical Imaging and Intensity-Modulated Therapy, IMRT, Edizioni della Norale, Pisa, Italy, pp 65–96 (2008)Google Scholar