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Theoretical and numerical comparison of relaxation methods for mathematical programs with complementarity constraints

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Abstract

Mathematical programs with equilibrium constraints (MPECs) are difficult optimization problems whose feasible sets do not satisfy most of the standard constraint qualifications. Hence MPECs cause difficulties both from a theoretical and a numerical point of view. As a consequence, a number of MPEC-tailored solution methods have been suggested during the last decade which are known to converge under suitable assumptions. Among these MPEC-tailored solution schemes, the relaxation methods are certainly one of the most prominent class of solution methods. Several different relaxation schemes are available in the meantime, and the aim of this paper is to provide a theoretical and numerical comparison of these schemes. More precisely, in the theoretical part, we improve the convergence theorems of several existing relaxation methods. There, we also take a closer look at the properties of the feasible sets of the relaxed problems and show which standard constraint qualifications are satisfied for these relaxed problems. Finally, the numerical comparison is based on the MacMPEC test problem collection.

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Authors and Affiliations

  1. Institute of Mathematics, University of Würzburg, Campus Hubland Nord, Emil-Fischer-Str. 30, 97074, Würzburg, Germany

    Tim Hoheisel, Christian Kanzow & Alexandra Schwartz

Authors
  1. Tim Hoheisel
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  2. Christian Kanzow
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  3. Alexandra Schwartz
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Correspondence to Christian Kanzow.

Additional information

This research was partially supported by a grant from the international doctorate program “Identification, Optimization, and Control with Applications in Modern Technologies” within the Elite-Network of Bavaria.

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Hoheisel, T., Kanzow, C. & Schwartz, A. Theoretical and numerical comparison of relaxation methods for mathematical programs with complementarity constraints. Math. Program. 137, 257–288 (2013). https://doi.org/10.1007/s10107-011-0488-5

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  • DOI: https://doi.org/10.1007/s10107-011-0488-5

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