Exact penalty functions for convex bilevel programming problems

In this paper, we propose a new constraint qualification for convex bilevel programming problems. Under this constraint qualification, a locally and globally exact penalty function of order I for a single-level reformulation of convex bilevel programming problems is given without requiring the linear independence condition and the strict complementarity condition to hold in the lower-level problem. Based on these results, locally and globally exact penalty functions for two other single-level reformulations of convex bilevel programming problems can be obtained. Furthermore, sufficient conditions for partial calmness to hold in some single-level reformulations of convex bilevel programming problems can be given.