Quadratic-form optimal transport is introduced, and for several cost classes including the rectangular cost, the unique minimizer is a new diamond-shaped coupling rather than the usual comonotone or antimonotone couplings.
For two random variables, we write the convex order relationZ⩽ cx WifE[h(Z)]⩽E[h(W)] for all convex functionshsuch that the two expectations are well-defined
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Quadratic-form Optimal Transport
Quadratic-form optimal transport is introduced, and for several cost classes including the rectangular cost, the unique minimizer is a new diamond-shaped coupling rather than the usual comonotone or antimonotone couplings.