Solving variational inequalities with a quadratic cut method: a primal-dual, Jacobian-free approach

We extend in two directions the Analytic Center, Cutting Plane Method for Variational Inequalities with quadratic cuts, ACCPM-VI(quadratic cuts), introduced by Denault and Go.n in 1998. First, we de9ne a primal–dual method to 9nd the analytic center at each iteration. Second, the Broyden–Fletcher–Goldfarb– Shanno Jacobian approximation, of quasi-Newton fame, is used in the de9nition of the cuts, making the algorithm applicable to problems without tractable Jacobians. The algorithm is tested on a variety of variational inequality problems, including one challenging problem of pricing the pollution permits put forward in the Kyoto Protocol. ? 2003 Elsevier Ltd. All rights reserved.