Pessimistic Bilevel Optimization
Name
Wiesemann-2013-Pessimistic bilevel optimization.pdf
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Author(s)
Wiesemann, Wolfram
Tsoukalas, Angelos
Kleniati, Polyxeni-Margarita
Rustem, Berc
Date Issued
February 2013
Journal
SIAM Journal on Optimization
Publisher
Society for Industrial and Applied Mathematics
Citation
Wiesemann, Wolfram, Angelos Tsoukalas, Polyxeni-Margarita Kleniati, and Berç Rustem. “Pessimistic Bilevel Optimization.” SIAM Journal on Optimization 23, no. 1 (February 27, 2013): 353-380. © 2013, Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
We study a variant of the pessimistic bilevel optimization problem, which comprises constraints that must be satisfied for any optimal solution of a subordinate (lower-level) optimization problem. We present conditions that guarantee the existence of optimal solutions in such a problem, and we characterize the computational complexity of various subclasses of the problem. We then focus on problem instances that may lack convexity, but that satisfy a certain independence property. We develop convergent approximations for these instances, and we derive an iterative solution scheme that is reminiscent of the discretization techniques used in semi-infinite programming. We also present a computational study that illustrates the numerical behavior of our algorithm on standard benchmark instances.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/120864015
