  In this study, we propose a novel gap-constraint-based reformulation for
optimal control problems with equilibrium constraints (OCPECs). We show that
the proposed reformulation generates a new constraint system equivalent to the
original one but more concise and with favorable differentiability. Moreover,
constraint regularity can be recovered by a relaxation strategy. We show that
the gap constraint and its gradient can be evaluated efficiently. We then
propose a successive gap constraint linearization method to solve the
discretized OCPEC. We also provide an intuitive geometric interpretation of the
gap constraint. Numerical experiments validate the effectiveness of the
proposed reformulation and solution method.
