论文标题
加权几何平均值，最小介导的集合和最佳的简单二阶表示
Weighted Geometric Mean, Minimum Mediated Set, and Optimal Simple Second-Order Cone Representation
论文作者
论文摘要
我们研究加权几何平均值的最佳简单二阶表示（二阶表示的特定子类），事实证明，这与最小介导的集合密切相关。证明了最佳简单二阶表示大小的几个上限和上限。在双变量加权几何平均值（等效地，一维中介集）的情况下，我们能够证明最佳简单简单二阶表示的确切大小，并给出算法来计算一个。在大量情况下，提出了快速启发式算法和遍历算法来计算近似最佳的简单二阶表示。最后，提供了用于多项式优化，矩阵优化和量子信息的应用。
We study optimal simple second-order cone representations (a particular subclass of second-order cone representations) for weighted geometric means, which turns out to be closely related to minimum mediated sets. Several lower and upper bounds on the size of optimal simple second-order cone representations are proved. In the case of bivariate weighted geometric means (equivalently, one dimensional mediated sets), we are able to prove the exact size of an optimal simple second-order cone representation and give an algorithm to compute one. In the genenal case, fast heuristic algorithms and traversal algorithms are proposed to compute an approximately optimal simple second-order cone representation. Finally, applications to polynomial optimization, matrix optimization, and quantum information are provided.
