A note on D-gap functions for equilibrium problems

Abstract

The equilibrium problem (EP) can be formulated as an unconstrained minimization problem through the D-gap function. We present a descent type algorithm for solving EP based on the generalized D-gap function. We discuss the convergence properties of the proposed algorithm under suitable assumptions while supporting our approach with appropriate examples. We construct an error bound for the equilibrium problem interms of the generalized D-gap function which gives a significant modification to the error bound given by Konnov et al.

Keywords:

• D-gap function
• equilibrium problem
• strongly monotone
• error bound

AMS Subject Classifications:

• 90C33
• 49J40

Acknowledgements

We are very thankful to the referees whose constructive suggestions have greatly improved the presentation of this article.