Groupe d’études et de recherche en analyse des décisions

G-2002-58

Solving Variational Inequalities with a Quadratic Cut Method: A Primal-Dual, Jacobian-Free Approach

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The Analytic Center, Cutting Plane Method for Variational Inequalities with quadratic cuts, ACCPM-VI(quadratic cuts), was introduced in Denault and Goffin, 1998. In this paper, we extend the method in two directions. First, we define a primal-dual method to find the analytic center at each iteration. Second, the Broyden-Fletcher-Goldfarb-Shanno Jacobian approximation, of quasi-Newton fame, is used in the definition of the cuts, making the algorithm applicable to problems without tractable Jacobians.

The algorithm is tested on a variety of variational inequalities, including one challenging problem of pricing the pollution permits put forward in the Kyoto Protocol.

, 22 pages