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 important applications. It well known that if treated as standard nonlinear program, some usual constraint qualifications may fail. To deal issue, one could reformulate it disjunctive (MPDC). first survey recent results MPDC, then apply them to MPSC. Moreover, provide two types sufficient local error bound penalty One comes from directional quasi-normality other obtained via decomposition approach.