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On Bilevel Optimization with Inexact Follower

Author

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  • M. Hosein Zare

    (Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15260)

  • Oleg A. Prokopyev

    (Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15260)

  • Denis Sauré

    (Department of Industrial Engineering, University of Chile, 8370456 Santiago, Chile)

Abstract

Traditionally, in the bilevel optimization framework, a leader chooses her actions by solving an upper-level problem, assuming that a follower chooses an optimal reaction by solving a lower-level problem. However, in many settings, the lower-level problems might be nontrivial, thus requiring the use of tailored algorithms for their solution. More importantly, in practice, such problems might be inexactly solved by heuristics and approximation algorithms. Motivated by this consideration, we study a broad class of bilevel optimization problems where the follower might not optimally react to the leader’s actions. In particular, we present a modeling framework in which the leader considers that the follower might use one of a number of known algorithms to solve the lower-level problem, either approximately or heuristically. Thus, the leader can hedge against the follower’s use of suboptimal solutions. We provide algorithmic implementations of the framework for a class of nonlinear bilevel knapsack problem (BKP), and we illustrate the potential impact of incorporating this realistic feature through numerical experiments in the context of defender-attacker problems.

Suggested Citation

  • M. Hosein Zare & Oleg A. Prokopyev & Denis Sauré, 2020. "On Bilevel Optimization with Inexact Follower," Decision Analysis, INFORMS, vol. 17(1), pages 74-95, March.
    • Handle: RePEc:inm:ordeca:v:17:y:2020:i:1:p:74-95
    DOI: 10.1287/deca.2019.0392
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    References listed on IDEAS

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