Monomial tropical cones for multicriteria optimization

We introduce a special class of tropical cones which we call 'monomial tropical cones'. They arise as a helpful tool in the description of discrete multicriteria optimization problems. After an introduction to tropical convexity with an emphasis on these particular tropical cones, we explain the algorithmic implications. It leads to an efficient algorithm for computing all nondominated points of a discrete multicriteria optimization problem based on tropical convex hull computation. We finish with connections to commutative algebra.