Making Augmented Lagrangian Methods Computer Amenable for Equilibrium Problems

ABSTRACT

We develop three algorithms to solve the subproblems generated by the augmented Lagrangian methods introduced by Iusem-Nasri (2010) for the equilibrium problem. The first algorithm that we propose incorporates the Newton method and the other two are instances of the subgradient projection method. One of our algorithms is also capable of solving nondifferentiable equilibrium problems. Using well-known test problems, all algorithms introduced here are implemented and numerical results are reported to compare their performances.