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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 deÿne a primal-dual method to ÿnd the analytic center at each iteration. Second, the Broyden-Fletcher-Goldfarb-Shanno Jacobian approximation, of quasi-Newton fame, is used in the deÿnition of the cuts, making the algorithm applicable to problems without tractable Jacobians. The algorithm is tested on adoi:10.1016/s0305-0548(03)00032-7 fatcat:kjvtacxq6jejxb2s6qlbzh5psm