  A global optimization approach for solving non-monotone equilibrium problems
(EPs) is proposed. The class of (regularized) gap functions is used to
reformulate any EP as a constrained global optimization program and some bounds
on the Lipschitz constant of such functions are provided. The proposed global
optimization approach is a combination of an improved version of the
\texttt{DIRECT} algorithm, which exploits local bounds of the Lipschitz
constant of the objective function, with local minimizations. Unlike most
existing solution methods for EPs, no monotonicity-type condition is assumed in
this paper. Preliminary numerical results on several classes of EPs show the
effectiveness of the approach.
