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The trouble with the second quantifier

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  • Gerhard J. Woeginger

    (RWTH Aachen)

Abstract

We survey optimization problems that allow natural simple formulations with one existential and one universal quantifier. We summarize the theoretical background from computational complexity theory, and we present a multitude of illustrating examples. We discuss the connections to robust optimization and to bilevel optimization, and we explain the reasons why the operational research community should be interested in the theoretical aspects of this area.

Suggested Citation

  • Gerhard J. Woeginger, 2021. "The trouble with the second quantifier," 4OR, Springer, vol. 19(2), pages 157-181, June.
    • Handle: RePEc:spr:aqjoor:v:19:y:2021:i:2:d:10.1007_s10288-021-00477-y
    DOI: 10.1007/s10288-021-00477-y
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    References listed on IDEAS

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    1. Deineko, Vladimir G. & Woeginger, Gerhard J., 2006. "On the dimension of simple monotonic games," European Journal of Operational Research, Elsevier, vol. 170(1), pages 315-318, April.
    2. Matteo Fischetti & Ivana Ljubić & Michele Monaci & Markus Sinnl, 2017. "A New General-Purpose Algorithm for Mixed-Integer Bilevel Linear Programs," Operations Research, INFORMS, vol. 65(6), pages 1615-1637, December.
    3. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 135-153.
    4. Alberto Caprara & Margarida Carvalho & Andrea Lodi & Gerhard J. Woeginger, 2016. "Bilevel Knapsack with Interdiction Constraints," INFORMS Journal on Computing, INFORMS, vol. 28(2), pages 319-333, May.
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    Cited by:

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    2. Stefan Napel & Dominik Welter, 2021. "Simple Voting Games and Cartel Damage Proportioning," Games, MDPI, vol. 12(4), pages 1-18, October.

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