We consider the variational inequality problem, denoted by VIP(X,F) where F is a strongly monotone function and the convex set X is described by some inequality (and possibly equality) constraints. This problem is solved by a continuation (or interior-point) method, which solves a sequence of certain perturbed variational, inequality problems. These perturbed problems depend on a parameter μ > 0. It is shown that the perturbed problems have a unique solution for all values of μ > 0, and that any sequence generated by the continuation method converges to the unique solution of VIP(X,F) under a well-known linear independence constraint qualification (LICQ). We also discuss the extension of the continuation method to monotone variational inequalities and present some numerical results obtained with a suitable implementation of this method.
