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On Semi-discrete Monge–Kantorovich and Generalized Partitions

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  • Gershon Wolansky

    (Technion)

Abstract

We address the question of characterizing the set of points in $$m$$ m dimensional space for which there exists a partition of a given measure space into $$m$$ 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.

Suggested Citation

  • Gershon Wolansky, 2015. "On Semi-discrete Monge–Kantorovich and Generalized Partitions," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 359-384, May.
    • Handle: RePEc:spr:joptap:v:165:y:2015:i:2:d:10.1007_s10957-014-0661-0
    DOI: 10.1007/s10957-014-0661-0
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    Cited by:

    1. Gershon Wolansky, 2019. "Semi-discrete optimal transport," Papers 1911.04348, arXiv.org, revised Sep 2020.

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