论文标题
共享经济衰退锥的最小对凸组
Minimal pairs of convex sets which share a recession cone
论文作者
论文摘要
罗宾逊推出了一对凸套装的商空间，它们共享衰退锥体。在本文中，最小的无界凸组对，即鲁滨逊空间元素的最小表示。证明了具有最小对具有翻译特性的最小对的事实。在对二维集合对的情况下，给出了等效最小对的公式，提出了一对集合的最小值的标准，并降低了所有最小对。 Shephard - Weil-紧凑型凸组的多面汇总标准被推广到无限制的凸组集。显示了最小的无界凸集对Hartman对DC函数的最小表示的应用。给出了三维组的最小对示例。
Robinson introduced a quotient space of pairs of convex sets which share their recession cone. In this paper minimal pairs of unbounded convex sets, i.e. minimal representations of elements of Robinson's spaces are investigated. The fact that a minimal pair having property of translation is reduced is proved. In the case of pairs of two-dimensional sets a formula for an equivalent minimal pair is given, a criterion of minimality of a pair of sets is presented and reducibility of all minimal pairs is proved. Shephard--Weil--Schneider's criterion for polytopal summand of a compact convex set is generalized to unbounded convex sets. An application of minimal pairs of unbounded convex sets to Hartman's minimal representation of dc-functions is shown. Examples of minimal pairs of three-dimensional sets are given.
