Monotone Optimal Multipartitions Using Schur Convexity with Respect to Partial Orders
Monotone Optimal Multipartitions Using Schur Convexity with Respect to Partial Orders
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DOI：
10.1137/0406042
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发表时间：
1993-11
期刊：
影响因子：
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通讯作者：
F. Hwang;U. Rothblum;L. Shepp
中科院分区：
文献类型：
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作者：
F. Hwang;U. Rothblum;L. Shepp
在$（t，n，m）$-多重分割问题中，t个$nm$有序数的列表被分割成n个集合，每个集合包含来自每个列表的m个数字。目标是最大化某个目标函数，该函数取决于每个集合中元素的总和，称为配分函数。作者利用最近发展起来的关于偏序集的优化理论和Schur凸性研究了上述问题的最优多重划分。特别是，他们应用的结果来构建一类反例最近猜想的杜和黄，它断言（经典）舒尔凸函数可以被表征为分区功能的$（1，n，m）$-multipartitioning问题具有单调的最优解。
In a $( t,n,m )$-multipartitioning problem, t lists of $nm$ ordered numbers are partitioned into n sets, where each set contains m numbers from each list. The goal is to maximize some objective function that depends on the sum of the elements in each set and is called the partition function. The authors use the recently developed theory of majorization and Schur convexity with respect to partially ordered sets to study optimal multipartitions for the above problem. In particular, they apply the results to construct a class of counterexamples to a recent conjecture of Du and Hwang, which asserts that (classic) Schur convex functions can be characterized as the partition functions for $( 1,n,m )$-multipartitioning problems having monotone optimal solutions.