论文标题
在优化中产生的多面球
Polytopal balls arising in optimization
论文作者
论文摘要
我们研究了一个多型及其双重家族，这些家族出现在各种优化问题中，就像某些规范的单位球一样。这两个家族在HyperCube，$ \ infty $ norm的单位球及其双重交叉式托管（$ 1 $ -NORM）之间插值。我们赋予了两个多型家族的组合和几何特性，例如它们的$ f $ - 向量，它们的体积和边界的体积。
We study a family of polytopes and their duals, that appear in various optimization problems as the unit balls for certain norms. These two families interpolate between the hypercube, the unit ball for the $\infty$-norm, and its dual cross-polytope, the unit ball for the $1$-norm. We give combinatorial and geometric properties of both families of polytopes such as their $f$-vector, their volume, and the volume of their boundary.
