A half-space projection method for solving generalized Nash equilibrium problems

Abstract

The generalized Nash equilibrium problem (GNEP) is an n-person noncooperative game in which each player’s strategy set depends on the rivals’ strategy set. In this paper, we presented a half-space projection method for solving the quasi-variational inequality problem which is a formulation of the GNEP. The difference from the known projection methods is due to the next iterate point in this method is obtained by directly projecting a point onto a half-space. Thus, our next iterate point can be represented explicitly. The global convergence is proved under the minimal assumptions. Compared with the known methods, this method can reduce one projection of a vector onto the strategy set per iteration. Numerical results show that this method not only outperforms the known method but is also less dependent on the initial value than the known method.

Keywords:

• Generalized Nash equilibrium
• quasi-variational inequality
• convex programming
• projection methods
• pseudomonotone

Acknowledgements

The author wishes to express his gratitude to two anonymous referees for their valuable comments that are very helpful for us to improve this paper.

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This research was supported by the Natural Science Key Project of Sichuan Provincial Department of Education of China [grant number 15ZA0154]; the Scientific Research Foundation of China West Normal University [grant number 14E014]; the University Innovation Team Foundation of China West Normal University [grant number CXTD2014-4]; the National Natural Science Foundation of China [grant number 11371015].