A Path-Following Cutting Plane Method for some Monotone Variational Inequalities

Abstract

. The paper considers two cases of variational inequality problems. The first case involves an affine monotone operator over a convex set defined by a separation oracle. An interior-point algorithm that mixes an interior cutting plane method and a short-step path-following method will be presented. Its complexity will be established. The second case is an extension of the first and involves a nonlinear monotone operator defined over the same type of convex set. The algorithm for the latter case is different from the former one only in the path-following stage. Keywords. Monotone variational inequalities, interior-point methods, analytic center, cutting planes, potential function. MCS. 90C33, 90C25, 58E35. 1 This research is supported by the Natural Sciences and Engineering Research Council of Canada, grant number OPG0004152 and by the FCAR of Quebec. 2 Faculty of Management, McGill University, 1001 Sherbrooke West, Montreal, Quebec, Canada H3A 1G5 3 Faculty of Management, McGill..