Recent progress in direct methods for fast mixed-integer optimal control has led to an appreciation of linear programs with additional nonconvex structure as the core subproblems to be solved. In this talk, we are interested in the fast solution of a sequence of linear programs with complementarity constraints (LPCCs) and vanishing constraints (LPVCs). Addressing this issue, we present a new parametric active-set method and its implementation. We discuss stationarity properties of the obtained limit points, and give an outlook on the use of this method within a sequential linear-quadratic solver for MPCCs and MPVCs.