An Interior Point Algorithm for Variational Inequality Problems ∗

In this paper, a new interior algorithm for tracing the combined homotopy path of the variational inequality problems is proposed, and its global convergence is established under some conditions. The residual control criteria, which ensures that the obtained iterative points are interior points, is given by the condition that ensures the β-cone neighborhood to be included in the interior part of the feasible region. Hence, the algorithm avoids judging whether the iterative points are the interior points or not in every predictor step and corrector step of the Euler-Newton method so that the computation is reduced greatly. The preliminary numerical experiments demonstrate that the algorithm is efficient and promising. Mathematics Subject Classifications: 90C33, 90C30, 65C20, 65L05