论文标题
排名锥体产生的双曲线及其衍生性放松的自动形态
Automorphisms of rank-one generated hyperbolicity cones and their derivative relaxations
论文作者
论文摘要
如果其所有极端射线具有排名第一，则据说双曲线锥体是排名第一的（ROG），该等级是相对于基本双曲线多项式计算的。这是一类天然的双曲线锥，严格比ROG谱系锥更一般。在这项工作中，我们介绍了ROG双曲线锥及其衍生性放松的自动形态的研究。我们的主要结果之一指出，衍生物松弛的自动形态正是原始锥体固定一定方向的自动形态。作为一种应用，我们完全确定了非负轨道和阳性半数矩阵锥体的衍生物松弛的自态。更普遍地，我们还证明了光谱锥的自动形态与潜在的置换式设置之间的关系，这可能具有独立的利益。
A hyperbolicity cone is said to be rank-one generated (ROG) if all its extreme rays have rank one, where the rank is computed with respect to the underlying hyperbolic polynomial. This is a natural class of hyperbolicity cones which are strictly more general than the ROG spectrahedral cones. In this work, we present a study of the automorphisms of ROG hyperbolicity cones and their derivative relaxations. One of our main results states that the automorphisms of the derivative relaxations are exactly the automorphisms of the original cone fixing a certain direction. As an application, we completely determine the automorphisms of the derivative relaxations of the nonnegative orthant and of the cone of positive semidefinite matrices. More generally, we also prove relations between the automorphisms of a spectral cone and the underlying permutation-invariant set, which might be of independent interest.
