Pessimistic bi-level optimization

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Title: Pessimistic bi-level optimization
Authors: Wiesemann, W
Tsoukalas, A
Kleniati, P-M
Rustem, B
Item Type: Report
Abstract: We study a variant of the pessimistic bi-level optimization problem, which comprises constraints that must be satis ed 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-in nite programming. We also present a computational study that illustrates the numerical behavior of our algorithm on standard benchmark instances.
Issue Date: 1-Jan-2012
Publisher: Department of Computing, Imperial College London
Start Page: 1
End Page: 39
Journal / Book Title: Departmental Technical Report: 12/4
Copyright Statement: © 2012 The Author(s). This report is available open access under a CC-BY-NC-ND (
Publication Status: Published
Article Number: 12/4
Appears in Collections:Computing Technical Reports

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