A modified projection algorithm for constrained equilibrium problems

Abstract

Based on the constrained variational inequality problem considered by Censor, Gibali and Reich (Numerical Algorithms, 2012), we propose, the constrained equilibrium problem (CEP), which consists in finding a point in the intersection of two nonempty, closed and convex subsets of an Euclidean space, C and D, such that is a solution of an equilibrium problem on C. In this work, an algorithm using projections is proposed to solve (CEP). Convergence properties of the algorithm are established under mild assumptions. Some numerical results are reported.

Keywords:

• Projection method
• equilibrium problem
• constrained equilibrium problem
• split equilibrium problem

Acknowledgements

We would like to thank the anonymous referees whose comments and suggestions greatly improved this work.

Notes

No potential conflict of interest was reported by the authors.