A CONTINUATION METHOD FOR (STRONGLY) MONOTONE VARIATIONAL-INEQUALITIES

We consider the variational inequality problem, denoted by VIP(X,F), w hen F is a strongly monotone function and the convex set X is describe d 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 mu > 0. It is shown that the perturbed problems have a unique solution for all values of mu > 0, a nd that any sequence generated by the continuation method converges to the unique solution of VIP(X,F) under a well-known linear independenc e constraint qualification (LICQ). We also discuss the extension of th e continuation method to monotone variational inequalities and present some numerical results obtained with a suitable implementation of thi s method. (C) 1998 The Mathematical Programming Society, Inc. Publishe d by Elsevier Science B.V.