Polyhedral approximation of a convex function is shown to be controlled by the quantization error of the Monge-Ampère measure of its Legendre-Fenchel dual, yielding a k-center pruning algorithm.
Quantitative stability of optimal trans- port maps under variations of the target measure,
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Duality between polyhedral approximation of value functions and optimal quantization of measures
Polyhedral approximation of a convex function is shown to be controlled by the quantization error of the Monge-Ampère measure of its Legendre-Fenchel dual, yielding a k-center pruning algorithm.