COPT: CoordinatedOptimalTransportonGraphs SupplementaryMaterial SupplementOutline

Let A be the map from RX to RX Y that sends a function f on X to the function f(x) p P(x,y)onX Y. Similarly,let B bethemapfrom RY toRX Y thatsendsafunction gto g(y) p P(x,y). Combining these, we get exactly the stated formula. Here we elaborate further on COPT's optimization routine. As the objective Equation 3.1 is not globally convex, gradient descent can fall into local minima. But this requires anontrivialnumber (e.g.