On a Primal-Dual Analytic Center Cutting Plane Method for Variational Inequalities

We present an algorithm for variational inequalities VI( $$\mathcal{F}$$ , Y) that uses a primal-dual version of the Analytic Center Cutting Plane Method. The point-to-set mapping $$\mathcal{F}$$ is assumed to be monotone, or pseudomonotone. Each computation of a new analytic center requires at most four Newton iterations, in theory, and in practice one or sometimes two. Linear equalities that may be included in the definition of the set Yare taken explicitly into account. We report numerical experiments on several well—known variational inequality problems as well as on one where the functional results from the solution of large subproblems. The method is robust and competitive with algorithms which use the same information as this one.