  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.
