We study a mathematical program with switching constraints (MPSC). By introducing a suitable constraint qualification and an alternative stationarity concept, we derive necessary optimality conditions using D-directional upper convexificators and D-directional upper semi-regular convexificators, where D is a nonempty closed cone within the set of continuity directions for functions that may lack continuity. An illustrative example is provided.
GADHI et al. (Thu,) studied this question.