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 involves a nonlinear monotone operator defined over the same type of convex set. An interior-point algorithm which is a combination of a cutting plane method and a long-step path-following method and uses the Jacobian of the operator will be presented. It will be shown that this latter algorithm finds an approximate solution in finite time.
Paru en octobre 1997 , 30 pages