论文标题
非面部裸露面孔的奇异程度
Singularity degree of non-facially exposed faces
论文作者
论文摘要
在本文中，我们研究了锥体线性图像的面部结构。我们将圆锥形面部面的奇异性度定义为使用双锥体中暴露向量所需的最小步骤。我们表明，锥体的线性图像的奇异性度正是面部还原步骤的数量，以在相应的原始圆锥优化问题中获得最小的面部。该结果概括了一般面部还原算法的复杂性与DrusvyAtskiy，Pataki和Wolkowicz在线性转换下的锥图像的面部暴露与任意奇异性度之间的关系。我们以原始形式和零扎形式呈现我们的结果。作为副产品，我们表明，弦图下面的框架最多具有一个级别的应力矩阵。
In this paper, we study the facial structure of the linear image of a cone. We define the singularity degree of a face of a cone to be the minimum number of steps it takes to expose it using exposing vectors from the dual cone. We show that the singularity degree of the linear image of a cone is exactly the number of facial reduction steps to obtain the minimal face in a corresponding primal conic optimization problem. This result generalizes the relationship between the complexity of general facial reduction algorithms and facial exposedness of conic images under a linear transform by Drusvyatskiy, Pataki and Wolkowicz to arbitrary singularity degree. We present our results in the original form and also in its nullspace form. As a by-product, we show that frameworks underlying a chordal graph have at most one level of stress matrix.
