High-accuracy Computation of Rolling Friction Contact Problems

Our goal is to numerically solve optimization problems derived from a mechanical model of unilateral contact between solid bodies with rolling friction. The model is an optimization problem with a strictly convex quadratic objective function and a second-order cone of constraints that is not self-dual. The solver is an implementation of a primal-dual interior-point algorithm with the predictor-corrector scheme of Mehrotra extended to the second-order cone problem. We focused on analyzing the limits of numerical computation and proposed some treatments to achieve optimal solutions with ten significant digits of precision.