论文标题
Terracini凸
Terracini Convexity
论文作者
论文摘要
我们提出了邻居对非多层凸锥的概念的概括。尽管在文献中的非多层案例中可以使用邻居的定义，但它是相当限制的，因为它要求所有低维面是多面体的。我们的方法更加灵活，包括例如阳性矩阵的锥作为特殊情况（通常不是邻居）。由于其概念上的相似性与代数几何形状的Terracini引理的结论，我们认为Terracini凸度的概括。当且仅当它们是邻居时，多面体锥为陶土凸。更广泛地说，我们基于邻居锥，阳性半芬酸盐基质的锥线性图像以及陶土凸出超质性锥的衍生性弛豫，得出了许多非多层陶土凸锥的家族。为了证明我们在非多层案例中框架的实用性，我们基于磨牙膜的陶土性，对某些相反问题的半际弛豫的紧密度进行了特征。
We present a generalization of the notion of neighborliness to non-polyhedral convex cones. Although a definition of neighborliness is available in the non-polyhedral case in the literature, it is fairly restrictive as it requires all the low-dimensional faces to be polyhedral. Our approach is more flexible and includes, for example, the cone of positive-semidefinite matrices as a special case (this cone is not neighborly in general). We term our generalization Terracini convexity due to its conceptual similarity with the conclusion of Terracini's lemma from algebraic geometry. Polyhedral cones are Terracini convex if and only if they are neighborly. More broadly, we derive many families of non-polyhedral Terracini convex cones based on neighborly cones, linear images of cones of positive semidefinite matrices, and derivative relaxations of Terracini convex hyperbolicity cones. As a demonstration of the utility of our framework in the non-polyhedral case, we give a characterization based on Terracini convexity of the tightness of semidefinite relaxations for certain inverse problems.
