A Multi-Objective Interpretation of Optimal Transport

Johannes Schumacher

Journal of Optimization Theory and Applications, 2018, vol. 176, issue 1, No 6, 94-119

Abstract: 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.

Keywords: Multi-objective optimization; Optimal transport; Regularization; Iterative proportional fitting; Nonlinear Perron–Frobenius theory; 90C08; 90C29; 90C33; 91B14 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-017-1206-0

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