OPTIMAL PATHS RELATED TO TRANSPORT PROBLEMS
OPTIMAL PATHS RELATED TO TRANSPORT PROBLEMS
复制标题
与运输问题相关的最佳路径
DOI：
10.1142/s021919970300094x
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发表时间：
2003
影响因子：
1.6
通讯作者：
Qinglan Xia
中科院分区：
文献类型：
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作者：
Qinglan Xia
在Monge类型的运输问题中，运输图的总成本通常是距离的某个函数的积分，例如|X - y| p.在许多真实的应用中，实际成本可能自然地由运输路径决定。对于将两个物品运送到一个位置，“Y形”路径可能比“V形”路径更可取。在这里，我们证明了任何概率度量都可以通过一般最优运输路径运输到另一个概率度量，该路径由我们设置中的向量度量给出。此外，我们在概率测度空间上定义了一个新的距离，它实际上度量了测度的弱 * 拓扑。在这个距离之下，概率测度的空间变成了一个长度空间。最后讨论了运输路径与运输规划的关系及相关问题。
In transport problems of Monge's types, the total cost of a transport map is usually an integral of some function of the distance, such as |x - y|p. In many real applications, the actual cost may naturally be determined by a transport path. For shipping two items to one location, a "Y shaped" path may be preferable to a "V shaped" path. Here, we show that any probability measure can be transported to another probability measure through a general optimal transport path, which is given by a vector measure in our setting. Moreover, we define a new distance on the space of probability measures which in fact metrizies the weak * topology of measures. Under this distance, the space of probability measures becomes a length space. Relations as well as related problems about transport paths and transport plans are also discussed in the end.