  Switching-constrained optimization problems form a difficult class of
mathematical programs since their feasible set is almost disconnected while
standard constraint qualifications are likely to fail at several feasible
points. That is why the application of standard methods from nonlinear
programming does not seem to be promising in order to solve such problems. In
this paper, we adapt the relaxation method from Kanzow and Schwartz (SIAM J.
Optim., 23(2):770-798, 2013) for the numerical treatment of mathematical
programs with complementarity constraints to the setting of
switching-constrained optimization. It is shown that the proposed method
computes M-stationary points under mild assumptions. Furthermore, we comment on
other possible relaxation approaches which can be used to tackle mathematical
programs with switching constraints. As it turns out, adapted versions of
Scholtes' global relaxation scheme as well as the relaxation scheme of
Steffensen and Ulbrich only find W-stationary points of switching-constrained
optimization problems in general. Some computational experiments visualize the
performance of the proposed relaxation method.
