On global partial calmness for bilevel programming problems with linear lower-level problem

Abstract

We consider bilevel programs such that their lower level problem is linear with respect to the lower level variable. It is known that such programs are partially calm and, therefore, can be reduced to a one level optimization problem by means of local penalization. One of the goals of our paper is to show that these programs can be reduced to a one level optimization problem via a global exact penalization. In the paper we also prove sufficient conditions of partial calmness for bilevel programs and study the pseudo-Lipschitzian continuity (Aubin property) of the solution mapping of the lower level problem.