Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Verification theorem and construction of $\epsilon$-optimal controls for
  control of abstract evolution equations   We study several aspects of the dynamic programming approach to optimal
control of abstract evolution equations, including a class of semilinear
partial differential equations. We introduce and prove a verification theorem
which provides a sufficient condition for optimality. Moreover we prove sub-
and superoptimality principles of dynamic programming and give an explicit
construction of $\epsilon$-optimal controls.

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The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg