Solution of Some Transportation Problems with Relaxed or Additional Constraints
Solution of Some Transportation Problems with Relaxed or Additional Constraints
复制标题
一些放松或附加约束的交通问题的解决
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
L. Rüschendorf
中科院分区：
文献类型：
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作者：
S. Rachev;L. Rüschendorf
作者考虑了通常运输问题的一些修改，分别考虑了允许的供给和需求分布的边界。特别地，考虑了供给的边际分布函数的下限是df F_1，而需求的边际分布函数的上限是df。对于边际差是固定的情况——这是著名的Kantorovich-Rubinstein问题的扩展——作者即使没有假设成本函数是Monge型，也得到了新的和一般的显式结果和界。还讨论了多变量的情况。在最后一节中，作者研究了具有局域约束的Monge-Kantorovich问题，即关于边界密度的问题。特别地，对关于最优耦合的经典Dobrushin定理进行了关于总变分的推广。
The authors consider some modifications of the usual transportation problem by allowing bounds for the admissible supply--- respectively, demand---distributions. In particular, the case that the marginal distribution function of the supply is bounded below by a $df F_1$, while the marginal $df$ of the demand is bounded above by a $df$ is considered. For the case that the difference of the marginals is fixed---this is an extension of the well-known Kantorovich-Rubinstein problem---the authors obtain new and general explicit results and bounds, even without the assumption that the cost function is of Monge type. The multivariate case is also treated. In the last section, the authors study Monge-Kantorovich problems with constraints of a local type, that is, on the densities of the marginals. In particular, the classical Dobrushin theorem on optimal couplings is extended with respect to total variation.