Semi-dual optimal transport has a degenerate saddle-point structure equivalent to constrained optimization, with necessary and sufficient conditions derived for Monge map convergence independent of dual potential optimality.
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Stability of the Monge Map in Semi-Dual Optimal Transport
Semi-dual optimal transport has a degenerate saddle-point structure equivalent to constrained optimization, with necessary and sufficient conditions derived for Monge map convergence independent of dual potential optimality.