# Monomial tropical cones for multicriteria optimization

arXiv: https://arxiv.org/abs/1707.09305 · HTML: https://mlsanity.com/paper/1707.09305/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jul 2017.

## Built on by (most cited first, 1 of 1)

- [Alternating Minimization for Regression with Tropical Rational Functions](https://mlsanity.com/paper/2305.20072/) (2023)

## Abstract (arXiv)

We present an algorithm to compute all n nondominated points of a multicriteria discrete optimization problem with d objectives using at most O(nlfloor d/2 rfloor) scalarizations. The method is similar to algorithms by Przybylski et al. (2010) and by Klamroth et al. (2015) with the same complexity. As a difference, our method employs a tropical convex hull computation, and it exploits a particular kind of duality which is special for the tropical cones arising. This duality can be seen as a generalization of the Alexander duality of monomial ideals.