Mathematical Sciences: On Monge-Kantorovich Problems

Monge.Kantorovich问题（MKPs）处理“最优”问题， 两个或多个等体积质量之间的对应关系 在一个抽象空间上，最优性取决于 问题的背景。 MKPs有着悠久而丰富多彩的历史， 数学科学的不同领域，因为他们的原始 由G. Monge（1781）和L.V. Kantorovich（1940）。 尽管存在特定MKP的单独结果， 已经进行了认真的尝试，以探索之间的相互作用， 各种方法。 本课题的目的是对这一问题进行系统的研究 的方法和结果之间的关系， MKP的“连续病例”。边际和矩问题 概率和那些在“离散情况”中的。优化 运输多面体和公理化方法， 测量问题。 校长认为 研究人员认为，算法和公理化的方法， 离散的情况下有很大的希望获得明确的解决方案 对于连续的MKP。 对称地， 概率。极限定理，正常和稳定的模型。将 导致识别新的数学规划， 离散博弈论结构、算法和模型 案子

Monge.Kantorovich problems (MKPs) deal with "optimal" correspondences between two or more masses of equal volume given on an abstract space, where the optimality depends upon the context of the problem. MKPs have a long and colorful history in different areas of mathematical sciences since their original formulation by G. Monge (1781) and L.V. Kantorovich (1940). Despite the existence of separate results for particular MKPs no serious attempt has been made to explore the interplay among the various approaches. The objective of this project is to make a systematic study of the relationships between the methods and results in the "continuous case" of MKPs . marginal and moment problems in probability . and those in the "discrete case" . optimization over transportation polytopes and axiomatic approaches to measurement problems. It is the belief of the principal investigators that the algorithms and axiomatic approaches of the discrete case hold great promise in obtaining explicit solutions for continuous MKPs. Symmetrically, the methods of probability .limit theorems, normal and stable models . will lead to the identification of new mathematical programming and game theoretic structures, algorithms and models in the discrete case.