Abstract
We consider the tropical analogues of a particular bilevel optimization problem studied by Dempe and Franke [4] and suggest some methods of solving these new tropical bilevel optimization problems. In particular, it is found that the algorithm developed by Dempe and Franke can be formulated and its validity can be proved in a more general setting, which includes the tropical bilevel optimization problems in question. We also show how the feasible set can be decomposed into a finite number of tropical polyhedra, to which the tropical linear programming solvers can be applied.
Supported by EPSRC grant EP/P019676/1.
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Notes
- 1.
In other words, \(e^{f(x,y)}\) is continuous and the sets \(\{y\in \mathbb {R}_+^n:\log (y)\in {\text {TP}}_1\}\) and \(\{z\in \mathbb {R}_+^n:\log (z)\in {\text {TP}}_1\}\) are compact in the usual Euclidean topology.
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Sergeev, S., Liu, Z. (2020). Tropical Analogues of a Dempe-Franke Bilevel Optimization Problem. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_69
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