Optimality Conditions and Exact Penalty for Mathematical Programs with Switching Constraints

In this paper, we give an overview on optimality conditions and exact penalization for the mathematical program with switching constraints (MPSC). MPSC is a new class of optimization problems which has some important applications. It is well-known that if MPSC is treated as a standard nonlinear program, some of the usual constraint qualifications may fail and to deal with this issue one could reformulate it as a mathematical program with disjunctive constraints (MPDC). In this paper we first survey recent results on constraint qualifications and optimality conditions for MPDC and then apply them to MPSC to obtain the corresponding constraint qualifications and optimality conditions. Moreover we provide two types of sufficient conditions for the local error bound and exact penalty results for MPSC. One comes from the directional quasi-normality for MPDC and the other is obtained by using the local decomposition approach.