An algorithm for a bilevel problem with equilibrium and fixed point constraints

Abstract

We prove the solution existence and propose an iterative algorithm for solving equilibrium problems over the common solutions of a monotone equilibrium problem and the fixed points of a strictly pseudocontractive mapping in Hilbert spaces. The algorithm is a combination of the proximal point and Halpern methods. Strong convergence is established.

Keywords:

• bilevel equilibria
• fixed point
• strict pseudocontraction
• strong pseudomonotonicity
• solution existence
• algorithm

AMS Subject Classifications:

• 47J05
• 47J06
• 47H06
• 49J30
• 90C25

Acknowledgements

The author would like to thank the Associate Editor and the referees for their helpful comments and remarks on the paper. This work is supported by the NAFOSTED, Vietnam.