No-gap second-order conditions for transport-regularized measure optimization are equivalent to quadratic growth once the Kantorovich potential satisfies a quadratic-growth regularity assumption.
Second Order Analysis for Bang-Bang Control Problems of PDEs
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No-gap second-order conditions for optimization problems involving transport distances
No-gap second-order conditions for transport-regularized measure optimization are equivalent to quadratic growth once the Kantorovich potential satisfies a quadratic-growth regularity assumption.