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.

KEYWORDS:

• Augmented Lagrangian
• Equilibrium problem
• Nash equilibrium problem
• Newton method
• Subgradient projection method

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of the last two authors was partially supported by CAPES.