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Theoretical and numerical comparison of the Karush–Kuhn–Tucker and value function reformulations in bilevel optimization
- Source :
- Computational Optimization and Applications. 78:625-674
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- The Karush-Kuhn-Tucker and value function (lower-level value function, to be precise) reformulations are the most common single-level transformations of the bilevel optimization problem. So far, these reformulations have either been studied independently or as a joint optimization problem in an attempt to take advantage of the best properties from each model. To the best of our knowledge, these reformulations have not yet been compared in the existing literature. This paper is a first attempt towards establishing whether one of these reformulations is best at solving a given class of the optimistic bilevel optimization problem. We design a comparison framework, which seems fair, considering the theoretical properties of these reformulations. This work reveals that although none of the models seems to particularly dominate the other from the theoretical point of view, the value function reformulation seems to numerically outperform the Karush-Kuhn-Tucker reformulation on a Newton-type algorithm. The computational experiments here are mostly based on test problems from the Bilevel Optimization LIBrary (BOLIB).<br />33 pages, 4 figures
- Subjects :
- Mathematical optimization
Class (set theory)
021103 operations research
Control and Optimization
Optimization problem
Karush–Kuhn–Tucker conditions
Applied Mathematics
Mathematics::Optimization and Control
0211 other engineering and technologies
010103 numerical & computational mathematics
02 engineering and technology
01 natural sciences
Bilevel optimization
Computational Mathematics
symbols.namesake
Optimization and Control (math.OC)
Bellman equation
FOS: Mathematics
symbols
Point (geometry)
0101 mathematics
Mathematics - Optimization and Control
Newton's method
Mathematics
Subjects
Details
- ISSN :
- 15732894 and 09266003
- Volume :
- 78
- Database :
- OpenAIRE
- Journal :
- Computational Optimization and Applications
- Accession number :
- edsair.doi.dedup.....3a64bfa1afd4579fd4a6a6842ce5e26b