Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean-Field Pontryagin Maximum Principle   We derive a Maximum Principle for optimal control problems with constraints
given by the coupling of a system of ODEs and a PDE of Vlasov-type. Such
problems arise naturally as ${\Gamma}$-limits of optimal control problems
subject to ODE constraints, modeling, for instance, external interventions on
crowd dynamics. We obtain these first-order optimality conditions in the form
of Hamiltonian flows in the Wasserstein space of probability measures with
forward-backward boundary conditions with respect to the first and second
marginals, respectively. In particular, we recover the equations and their
solutions by means of a constructive procedure, which can be seen as the
mean-field limit of the Pontryagin Maximum Principle applied to the discrete
optimal control problems, under a suitable scaling of the adjoint variables.

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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nlin