Mathematical Sciences: On Monge-Kantorovich Problems

数学科学：关于 Monge-Kantorovich 问题

• 批准号: 8902330
• 负责人: Michel Balinski
• 金额: $ 2.73万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-08-01 至 1990-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902330&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Monge; Kantorovich; Problems

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.

Monge.Kantorovich问题（MKPS）处理在抽象空间上给出的两个或更多相等体积质量之间的“最佳”对应关系，其中最佳性取决于问题的上下文。 自G. Monge（1781）和L.V.的原始表述以来，MKP在数学科学的不同领域具有悠久而丰富多彩的历史。坎托维奇（1940）。 尽管存在特定MKP的单独结果，但尚未进行认真的尝试来探索各种方法之间的相互作用。 该项目的目的是系统地研究MKPS的“连续情况”的方法与结果之间的关系。概率的边际和力矩问题。以及“离散案例”中的那些。对运输多型和公理方法的优化，用于测量问题。 主要研究人员的信念是，离散案例的算法和公理方法在获得连续MKP的明确解决方案方面有很大的希望。 对称地，概率的方法限制定理，正常和稳定的模型。将导致在离散情况下识别新的数学编程和游戏理论结构，算法和模型。