# Tropical analogues of a Dempe-Franke bilevel optimization problem

## TL;DR

This paper extends bilevel optimization to tropical algebra, demonstrating that existing algorithms can be adapted and decomposing feasible sets into tropical polyhedra for solving these new problems.

## Contribution

It generalizes Dempe and Franke's algorithm to tropical bilevel problems and introduces a method to decompose feasible sets into tropical polyhedra.

## Key findings

- Dempe and Franke's algorithm applies to tropical bilevel problems
- Feasible sets can be decomposed into tropical polyhedra
- Tropical linear programming solvers are applicable

## 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.