An analytic center cutting plane algorithm for finding equilibrium points

We present a variant of the analytic center cutting plane algorithm proposed by Goffin et al. to approximately solve equilibrium problems as proposed by Blum and Oettli, which include as particular problems the variational inequalities problem, the Nash equilibria problem in non-cooperative games, the convex minimization problem, and the fixed point problem. Furthermore, we analyze the convergence and complexity of the modified algorithm.