面部暴露与漂亮视锥细胞的关系
On the connection of facially exposed and nice cones
摘要：
一个闭凸锥K称为nice，如果集合K^* + F^ \perp对于K的所有F面都是闭的，其中K^* 是K的对偶锥，F^ \perp是F的线性展长的正交补。niceness属性很重要，原因有二：它在Borwein和Wolkowicz的面部缩小算法中起作用，以及一个nice cone的线性图像是否闭合的问题也有一个简单的答案。我们证明了几个特征的尼斯锥，并显示出强大的连接与面部暴露。我们证明了一个很好的圆锥体必须是面部暴露，在相反的情况下，面部暴露与附加条件意味着niceness。我们推测，漂亮的，和面部暴露的锥体实际上是相同的，并给出支持证据。
英文摘要：
A closed convex cone K is called nice, if the set K^* + F^\perp is closed for all F faces of K, where K^* is the dual cone of K, and F^\perp is the orthogonal complement of the linear span of F. The niceness property is important for two reasons: it plays a role in the facial reduction algorithm of Borwein and Wolkowicz, and the question whether the linear image of a nice cone is closed also has a simple answer. We prove several characterizations of nice cones and show a strong connection with facial exposedness. We prove that a nice cone must be facially exposed; in reverse, facial exposedness with an added condition implies niceness. We conjecture that nice, and facially exposed cones are actually the same, and give supporting evidence.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
