# On minimal extended representations of generalized power cones

arXiv: https://arxiv.org/abs/2311.10470 · HTML: https://mlsanity.com/paper/2311.10470/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2023.

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

- [Exact Matrix Seriation through Mathematical Optimization: Stress and Effectiveness-Based Models](https://mlsanity.com/paper/2506.19821/) (2025)

## Abstract (arXiv)

In this paper, we analyze minimal representations of (p,boldsymbolα)-power cones as simpler cones. We derive some new results on the complexity of the representations, and we provide a procedure to construct a minimal representation by means of second order cones in case boldsymbolα and p are rational. The construction is based on the identification of the cones with a graph, the mediated graph. Then, we develop a mixed integer linear optimization formulation to obtain the optimal mediated graph, and then, the minimal representation. We present the results of a series of computational experiments in order to analyze the computational performance of the approach, both to obtain the representation and its incorporation into a practical conic optimization model that arises in facility location.