A projection algorithm for solving pseudomonotone equilibrium problems and it's application to a class of bilevel equilibria

Abstract

We propose a projection algorithm for solving an equilibrium problem (EP) where the bifunction is pseudomonotone with respect to its solution set. The algorithm is further combined with a cutting technique for minimizing the norm over the solution set of an EP whose bifunction is pseudomonotone with respect to the solution set.

Keywords:

• pseudomonotone equilibria
• Ky Fan inequality
• auxiliary subproblem principle
• projection method
• Armijo linesearch
• bilevel equilibria

AMS Subject Classifications:

• 2010
• 65 K10
• 90 C25

Acknowledgments

The authors would like to thank the referees for their helpful comments and remarks which helped them very much in revising the paper. This work is supported in part by the NAFOSTED, Vietnam under the grant 101.02-2011-19.