Tropical analogues of a Dempe-Franke bilevel optimization problem
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Abstract
We consider the tropical analogues of a particular bilevel optimization problem studied by Dempe and Franke 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.Keywords
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This publication has 6 references indexed in Scilit:
- Tropicalizing the Simplex AlgorithmSIAM Journal on Discrete Mathematics, 2015
- Solution algorithm for an optimistic linear Stackelberg problemComputers & Operations Research, 2014
- Tropical linear-fractional programming and parametric mean payoff gamesJournal of Symbolic Computation, 2012
- Computing the Vertices of Tropical Polyhedra Using Directed HypergraphsDiscrete & Computational Geometry, 2012
- Max-linear Systems: Theory and Algorithms2010
- On the equivalence of linear complementarity problemsOperations Research Letters, 2002