论文标题
在polyhedra的无界凸集近似值上
On the Approximation of Unbounded Convex Sets by Polyhedra
论文作者
论文摘要
本文与Polyhedra的无界凸集集有关。尽管有大量文献调查了这项任务的紧凑型组合，但无限案例的结果很少。我们首先指出现有结果之间的连接，然后再引入新的多面体近似概念（$ \ varepsilon，δ$） - 以有意义的方式集成了无限制的情况。有关（$ \ varepsilon，δ$）的一些基本结果 - 对于一般凸集证明了近似值。在最后一节中，用于计算（$ \ varepsilon，δ$）的算法 - 介绍了频谱的近似值。证明了算法的正确性和有限性。
This article is concerned with the approximation of unbounded convex sets by polyhedra. While there is an abundance of literature investigating this task for compact sets, results on the unbounded case are scarce. We first point out the connections between existing results before introducing a new notion of polyhedral approximation called ($\varepsilon,δ$)-approximation that integrates the unbounded case in a meaningful way. Some basic results about ($\varepsilon,δ$)- approximations are proven for general convex sets. In the last section an algorithm for the computation of ($\varepsilon,δ$)-approximations of spectrahedra is presented. Correctness and finiteness of the algorithm are proven.
