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

Michel Denault, J.-L. Goffin
2004 Computers & Operations Research  
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 a
more » ... variety of variational inequality problems, including one challenging problem of pricing the pollution permits put forward in the Kyoto Protocol. ?
doi:10.1016/s0305-0548(03)00032-7 fatcat:kjvtacxq6jejxb2s6qlbzh5psm