论文标题
在同等的表面和特性上
On equivalent representations and properties of faces of the cone of copositive matrice
论文作者
论文摘要
该论文致力于研究共同矩阵的锥体$ \ cop $。基于从半无动索引的半无限优化概念中的已知概念，我们定义了圆锥$ \ cop $的子集的零和最小零向量，并使用它们来获得$ \ cop $的面孔的不同表示和相应的双锥。我们描述了包含该锥体的给定凸子集的$ \ cop $的最小面孔，并证明了一些命题，这些命题允许获得同等的共同问题可行集合的相同描述，并且可能有助于根据其正则化创建新的数值方法。
The paper is devoted to a study of the cone $\cop$ of copositive matrices. Based on the known from semi-infinite optimization concept of immobile indices, we define zero and minimal zero vectors of a subset of the cone $\cop$ and use them to obtain different representations of faces of $\cop$ and the corresponding dual cones. We describe the minimal face of $\cop$ containing a given convex subset of this cone and prove some propositions that allow to obtain equivalent descriptions of the feasible sets of a copositive problems and may be useful for creating new numerical methods based on their regularization.
