Abstract
AbstractWe summarize the relations of optimality systems for an interacting particle dynamic in the microscopic and in the kinetic description. In particular, we answer the question if the passing to the mean‐field limit and deriving the first order optimality system can be interchanged without affecting the results. The answer is affirmative, if one derives the optimality system on the kinetic level in the metric space (𝒫2, 𝒲2). Moreover, we discuss the relation of to the adjoint PDE derived in the L2‐sense. Here, the gradient can be derived as expected from the calculus in Wasserstein space.
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