Characterization of the optimal plans for the Monge-Kantorovich transport problem

Details Characterization of the optimal plans for the Monge-Kantorovich transport problem Characterization of the optimal plans for the Monge-Kantorovich transport problem

2006-07-24

arxiv.org/abs/math/0607604v1

Mathematics

Optimization and Control

39 pages

Scientific paper

We present a general method, based on conjugate duality, for solving a convex minimization problem without assuming unnecessary topological restrictions on the constraint set. It leads to dual equalities and characterizations of the minimizers without constraint qualification. As an example of application, the Monge-Kantorovich optimal transport problem is solved in great detail. In particular, the optimal transport plans are characterized without restriction. This characterization improves the already existing literature on the subject.

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