极小双曲多项式与齐次锥的秩
最优化与控制
2025-06-13 v3 代数几何
度量几何
摘要
本文的出发点是计算由弦稀疏模式产生的锥的对偶的极小双曲多项式。由此，我们研究了齐次锥的秩与其极小多项式之间的关系。在此过程中，我们否定了先前论文中提出的一个问题，并展示了不能实现为秩一生成(ROG)双曲锥的齐次锥的例子。
引用
@article{arxiv.2404.03860,
title = {Minimal hyperbolic polynomials and ranks of homogeneous cones},
author = {João Gouveia and Masaru Ito and Bruno F. Lourenço},
journal= {arXiv preprint arXiv:2404.03860},
year = {2025}
}
备注
21 pages, 1 figure. To appear in the Journal of Convex Analysis. The question at the end was solved by Hideto Nakashima and we included some comments on the solution. Dedicated to Prof. R.T. Rockafellar on the occasion of his 90th birthday