We propose a new interior-point method for Mathematical Programs
with Equilibrium Constraints (MPECs). The approach makes use of a sequence of relaxed MPECs parameterized by a relaxation parameter vector and only performs
one log-barrier Newton step for each relaxed MPEC. Unlike previous approaches, the barrier and relaxation parameters are updated in such a way that the strict
interior of the relaxed MPEC remains nonempty even in the limit. We analyze the
convergence properties of the proposed algorithm.