A study of projectionally exposed cones
A study of projectionally exposed cones
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投影暴露锥体的研究
DOI：
10.1016/0024-3795(90)90401-w
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发表时间：
1990
影响因子：
1.1
通讯作者：
B. Tam
中科院分区：
文献类型：
--
作者：
C. Sung;B. Tam
Barker， Laidacker和Poole考虑到抽象凸规划的可能应用，通过将他们的注意力限制在闭合的尖锥上，对p-暴露锥和op -暴露锥进行了初步的研究。本文对这些锥体进行了进一步的研究。建立了适当锥面为p-暴露面或p-暴露面的充分条件。得到了多面体锥体中opp暴露锥体的特征。研究了一般锥体面曝光与p曝光之间的关系。作为一个结果，Iochum提出的问题在有限维情况下得到了回答；也就是说，不存在非正则的有限维半正则自对偶锥。在p (n)的p个暴露面上，Barker和Thompson提出了一个猜想，即在闭区间[0,1]上，所有阶为≤n的实多项式的非负多项式的锥是成立的。
In view of possible applications to abstract convex programs, Barker, Laidacker, and Poole have made an initial study of p-exposed cones and o.p.-exposed cones by restricting their attention to closed, pointed cones. A study of these cones is continued in this paper. Sufficient conditions for a face of a proper cone to be a p-exposed or an o.p.-exposed face are established. Characterizations of o.p.-exposed cones among polyhedral cones are also obtained. The relation between exposedness and p-exposedness of faces of a general cone is examined. As one consequence, a question posed by Iochum is answered in the finite dimensional case; that is, there is no finite-dimensional semiregular self-dual cones which are not regular. Also, a conjecture posed by Barker and Thompson on p-exposed faces ofP(n), that the cone of all real polynomials of degree⩽nwhich are nonnegative on the closed interval [0,1], is settled.