Smooth marginals induce non-degenerate curvature in the optimal transport functional w.r.t. the cost, enabling local identifiability and stability for inverse optimal transport.
Moreover,A7→T A 0 is invariant by positive translation:T λA 0 =T A 0 providedλ >0, because positively collinear matrices generate the same classic OT plan
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Curvature of optimal transport with respect to the cost and applications to inverse optimal transport
Smooth marginals induce non-degenerate curvature in the optimal transport functional w.r.t. the cost, enabling local identifiability and stability for inverse optimal transport.