Solving mathematical programs with complementarity constraints as nonlinear programs

Abstract

Abstract We consider solving mathematical programs with complementarity constraints (MPCCs) as nonlinear programs (NLPs) using standard NLP solvers. This approach is appealing because it allows existing off-the-shelf NLP solvers to tackle large instances of MPCCs. Numerical experience on MacMPEC, a large collection of MPCC test problems is presented. Our experience indicates that sequential quadratic programming (SQP) methods are very well suited for solving MPCCs and at present outperform interior-point solvers both in terms of speed and reliability. All NLP solvers also compare very favorably to special MPCC solvers on tests published in the literature. Keywords: MPCCComplementarity constraintsNonlinear programmingSequential quadratic programmingInterior-point methods Acknowledgments This work was supported EPSRC grant GR/M59549. We are also grateful for the opportunity to using Argonne's computing resources in carrying out our comparisons. We are grateful to Stefan Scholtes, Danny Ralph and Michael Ferris for many fruitful discussions on MPCCs. Finally, we gratefully acknowledge the insightful comments of an anonymous referee who greatly improved the article. Many individuals provided help and input for the problem library. We are grateful to David Gay for sharing his AMPL expertise with us. Michal Kocvara provided help with the packaging problems. Francis Tin Loi supplied some challenging structural engineering problems. Finally, we have 'borrowed' test problems from a variety of sources but most notably from MPECLIB of Steven Dirkse. Notes *[e-mail] ‡This work was carried out while the second author was at the University of Dundee. Additional informationNotes on contributorsRoger FletcherFootnote* *[e-mail] Sven Leyffer,Footnote‡ ‡This work was carried out while the second author was at the University of Dundee.