On Semi-discrete Monge–Kantorovich and Generalized Partitions

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• 作者：Gershon Wolansky
• 关键词：Optimal transport ; Monge–Kanotrovich ; Partitions
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2015
• 出版时间：May 2015
• 年：2015
• 卷：165
• 期：2
• 页码：359-384
• 全文大小：293 KB
• 参考文献：1. Monge, G.: Mémoire sur la théorie des déblais et des remblais, Histoire de lácadémie Royale des Sciences de Paris, pp. 666-04 (1781)
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  13. Ma, XN, Trudinger, NS, Wang, XJ (2005) Regularity of potential functions of the optimal transportation problem. Arch. Ration. Mech. Anal. 177: pp. 151-183 CrossRef
  
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878

文摘

We address the question of characterizing the set of points in \(m\) dimensional space for which there exists a partition of a given measure space into \(m\) essentially disjoint sets satisfying prescribed integral conditions. In addition, we discuss some optimization problems on this set of partitions. The relation of this problem to the semi-discrete version of optimal mass transportation is discussed as well.