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On Semi-discrete Monge–Kantorovich and Generalized Partitions

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Abstract

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.

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Notes

  1. Traditionally, the MK problem deals with minimization of the cost. In the current setting, it is more natural to talk about maximization. The two options are, of course, equivalent under a sign change of the cost \(c\).

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Acknowledgments

This research was partially supported by the ISF research Grant #481/09 and BSF Grant #2018214.

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Authors and Affiliations

  1. Department of Mathematics, Technion, 32000, Haifa, Israel

    Gershon Wolansky

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  1. Gershon Wolansky
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Correspondence to Gershon Wolansky.

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Communicated by Hedy Attouch.

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Wolansky, G. On Semi-discrete Monge–Kantorovich and Generalized Partitions. J Optim Theory Appl 165, 359–384 (2015). https://doi.org/10.1007/s10957-014-0661-0

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  • DOI: https://doi.org/10.1007/s10957-014-0661-0

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