An analytic center cutting plane algorithm for finding equilibrium points

TL;DR: A variant of the analytic center cutting plane algorithm proposed by Goffin et al. (1996) to approximately solve equi- librium problems as proposed by Blum and Oettli (1994), 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.

Abstract: We present a variant of the analytic center cutting plane algorithm proposed by Goffin et al. (1996) to approximately solve equi- librium problems as proposed by Blum and Oettli (1994), 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.