# American Institute of Mathematical Sciences

July  2016, 12(3): 879-890. doi: 10.3934/jimo.2016.12.879

## An augmented Lagrangian-based parallel splitting method for a one-leader-two-follower game

 1 Department of Mathematics, Taiyuan Normal University, Taiyuan 030012, Shanxi Province, China

Received  February 2014 Revised  November 2014 Published  September 2015

In this paper, we exploit a new parallel splitting method for the typical structured variational inequality problems which can be interpreted as a game with a leader and two followers. In the framework of this method, two followers decide their strategies simultaneously based on the instruction of the leader. Then, the leader improves his instruction by revising his own variable value according to the feedback information from the followers. The convergence of the method is established under some suitable conditions. Finally, we apply the proposed method to solve some application problems. Computational studies show that the method is reliable and efficient.
Citation: Xihong Yan. An augmented Lagrangian-based parallel splitting method for a one-leader-two-follower game. Journal of Industrial & Management Optimization, 2016, 12 (3) : 879-890. doi: 10.3934/jimo.2016.12.879
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