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MPEC Methods for Bilevel Optimization Problems

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Bilevel Optimization

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 161))

Abstract

We study optimistic bilevel optimization problems, where we assume the lower-level problem is convex with a nonempty, compact feasible region and satisfies a constraint qualification for all possible upper-level decisions. Replacing the lower-level optimization problem by its first-order conditions results in a mathematical program with equilibrium constraints (MPEC) that needs to be solved. We review the relationship between the MPEC and bilevel optimization problem and then survey the theory, algorithms, and software environments for solving the MPEC formulations.

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Acknowledgements

This work was supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research under Contract No. DE-AC02-06CH11357 at Argonne National Laboratory.

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  1. Argonne National Laboratory, Lemont, IL, USA

    Youngdae Kim, Sven Leyffer & Todd Munson

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  1. Youngdae Kim
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  1. Institute of Numerical Mathematics and Optimization, TU Bergakademie Freiberg, Freiberg, Germany

    Stephan Dempe

  2. School of Mathematical Sciences, University of Southampton, Southampton, UK

    Alain Zemkoho

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Kim, Y., Leyffer, S., Munson, T. (2020). MPEC Methods for Bilevel Optimization Problems. In: Dempe, S., Zemkoho, A. (eds) Bilevel Optimization. Springer Optimization and Its Applications, vol 161. Springer, Cham. https://doi.org/10.1007/978-3-030-52119-6_12

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