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A Multi-Objective Interpretation of Optimal Transport

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  • Johannes M. Schumacher

    (University of Amsterdam)

Abstract

This paper connects discrete optimal transport to a certain class of multi-objective optimization problems. In both settings, the decision variables can be organized into a matrix. In the multi-objective problem, the notion of Pareto efficiency is defined in terms of the objectives together with nonnegativity constraints and with equality constraints that are specified in terms of column sums. A second set of equality constraints, defined in terms of row sums, is used to single out particular points in the Pareto-efficient set which are referred to as “balanced solutions.” Examples from several fields are shown in which this solution concept appears naturally. Balanced solutions are shown to be in one-to-one correspondence with solutions of optimal transport problems. As an example of the use of alternative interpretations, the computation of solutions via regularization is discussed.

Suggested Citation

  • Johannes M. Schumacher, 2018. "A Multi-Objective Interpretation of Optimal Transport," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 94-119, January.
    • Handle: RePEc:spr:joptap:v:176:y:2018:i:1:d:10.1007_s10957-017-1206-0
    DOI: 10.1007/s10957-017-1206-0
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    References listed on IDEAS

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