An optimal matching problem

Details An optimal matching problem An optimal matching problem

2003-08-21

arxiv.org/abs/math/0308206v1

Mathematics

Optimization and Control

Scientific paper

Given two measured spaces (X,dx), (Y,dy) and a third space Z, given two
functions u(x,z) and v(x,z), we study the problem of finding two maps s from X
to Z and t from Y to Z such that the images s(dx) and t(dy) coincide, and the
integral of u(x,s(x))dx+v(y,t(y))dy is maximal. We give condition on u and v
for which there is a unique solution.

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