Optimal solutions of multivariate coupling problems
Optimal solutions of multivariate coupling problems
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多元耦合问题的最优解
DOI：
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发表时间：
1995
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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：
L. Rüschendorf
建立了多元运输(耦合)问题最优解的显式构造和刻画的一些充要条件和一些充分条件。证明基于对偶论和非凸最优化理论的思想。给出了多元最优耦合问题的应用。极小p-型度量，其中得到了最优运输计划(耦合)的相当明确和完整的刻画。即使在一维的情况下，结果也是很有意义的。首次给出了构造Kantorovich度量的最优多元耦合的一个显式准则。
Some necessary and some suucient conditions are established for the explicit construction and characterization of optimal solutions of multivariate transportation (coupling) problems. The proofs are based on ideas from duality theory and nonconvex optimization theory. Applications are given to multivariate optimal coupling problems w.r.t. minimaì p-type metrics, where fairly explicit and complete characterizations of optimal transportation plans (couplings) are obtained. The results are of interest even in the one-dimensional case. For the rst time an explicit criterion is given for the construction of optimal multivariate couplings for the Kantorovich metric`1 .