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Regularizing Bilevel Nonlinear Programs by Lifting

Kathrin Hatz(kathrin.hatz***at***iwr.uni-heidelberg.de)
Sven Leyffer(leyffer***at***mcs.anl.gov)
Johannes P. Schloeder(Schloeder***at***IWR.Uni-Heidelberg.De)
Hans Georg Bock(SciCom***at***IWR.Uni-Heidelberg.De)

Abstract: 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.

Keywords: nonlinear programming, bilevel optimization, lifting bilevel programs, mathematical programs with equilibrium constraints, mathematical programs with complementarity constraints

Category 1: Nonlinear Optimization

Category 2: Complementarity and Variational Inequalities

Citation: Preprint ANL/MCS-P4076-0613, Argonne National Laboratory, Mathematics and Computer Science Division, June 2013

Download: [PDF]

Entry Submitted: 06/10/2013
Entry Accepted: 06/10/2013
Entry Last Modified: 06/10/2013

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