Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Pontryagin Maximum Principle in the Wasserstein Space   We prove a Pontryagin Maximum Principle for optimal control problems in the
space of probability measures, where the dynamics is given by a transport
equation with non-local velocity. We formulate this first-order optimality
condition using the formalism of subdifferential calculus in Wasserstein
spaces. We show that the geometric approach based on needle variations and on
the evolution of the covector (here replaced by the evolution of a mesure on
the dual space) can be translated into this formalism.

10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg