Interactive rigid body simulation is important for robot simulation and virtual design. A vital part of the simulation is the computation of contact forces. This paper addresses the contact force problem, as used in interactive simulation. Contact forces are applied to prevent rigid bodies from penetrating and to control slipping between bodies. Accurate contact force determination is a computationally hard problem. Thus, in practice one trades accuracy for performance. This results in visual artefacts such as viscous or damped contact response. In this paper, we present a new approach to contact force determination. We formulate the contact force problem as a nonlinear complementarity problem, and discretize the problem to derive the Projected Gauss-Seidel method. We combine the Projected Gauss-Seidel method with a subspace minimization method. Our new method shows improved qualities and superior convergence properties for specific configurations.