Regularizing Bilevel Nonlinear Programs by Lifting
|Title||Regularizing Bilevel Nonlinear Programs by Lifting|
|Publication Type||Journal Article|
|Year of Publication||2013|
|Authors||Hatz, K, Leyffer, S, Schloder, JP, Bock, HG|
|Journal||SIAM Journal on Optimization|
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.