This paper considers a bilevel nonlinear program (NLP) whose lower-level problem satisfies a linear independence constraint qualification (LICQ) and a strong second-order condition (SSOC). One would expect the resulting mathematical program with complementarity constraints (MPCC), whose constraints are the first-order optimality conditions of the lower-level NLP, to satisfy an MPEC-LICQ. We provide an example which demonstrates that this is not the case. A lifting technique is presented to remedy this problem.
Preprint ANL/MCS-P4076-0613, Argonne National Laboratory, Mathematics and Computer Science Division, June 2013