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Optimization with Multivalued Mappings pp 169–208Cite as

Complementarity constraints as nonlinear equations: Theory and numerical experience

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 2))

Summary

Recently, it has been shown that mathematical programs with complementarity constraints (MPCCs) can be solved efficiently and reliably as nonlinear programs. This paper examines various nonlinear formulations of the complementarity constraints. Several nonlinear complementarity functions are considered for use in MPCC. Unlike standard smoothing techniques, however, the reformulations do not require the control of a smoothing parameter. Thus they have the advantage that the smoothing is exact in the sense that Karush-Kuhn-Tucker points of the reformulation correspond to strongly stationary points of the MPCC. A new exact smoothing of the well-known min function is also introduced and shown to possess desirable theoretical properties. It is shown how the new formulations can be integrated into a sequential quadratic programming solver, and their practical performance is compared on a range of test problems.

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Author information

Authors and Affiliations

  1. Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, 60439, USA

    Sven Leyffer

Authors
  1. Sven Leyffer
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Editor information

Editors and Affiliations

  1. TU Bergakademie Freiberg, Germany

    Stephan Dempe

  2. ITESM, Monterrey, Mexico

    Vyacheslav Kalashnikov

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© 2006 Springer Science + Business Media, LLC

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Leyffer, S. (2006). Complementarity constraints as nonlinear equations: Theory and numerical experience. In: Dempe, S., Kalashnikov, V. (eds) Optimization with Multivalued Mappings. Springer Optimization and Its Applications, vol 2. Springer, Boston, MA . https://doi.org/10.1007/0-387-34221-4_9

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