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. A componentwise lifting of the inequality constraints of the lower-level problem implies that the resulting MPCC satisfies an MPCC-LICQ which leads to a faster convergence. We generalize the lifting approach to general MPCCs. Convergence results and numerical experiments are provided that show the promise of our approach.

%B SIAM Journal on Optimization %G eng %1 http://www.mcs.anl.gov/papers/P4076-0613_1.pdf