Pessimistic bi-level optimization
File(s)
Published version
Author(s)
Wiesemann, Wolfram
Tsoukalas, Angelos
Kleniati, Polyxeni-Margarita
Rustem, Berc
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.
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.
Date Issued
2012-01-01
Citation
Departmental Technical Report: 12/4, 2012, pp.1-39
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 (https://creativecommons.org/licenses/by-nc-nd/4.0/)
Publication Status
Published
Article Number
12/4