Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: First-order conditions for the optimal control of the obstacle problem
  with state constraints   We consider an optimal control problem in which the state is governed by an
unilateral obstacle problem (with obstacle from below) and restricted by a
pointwise state constraint (from above). In the presence of control
constraints, we prove, via regularization of the state constraints, that a
system of C-stationarity is necessary for optimality. In the absence of control
constraints, we show that local minimizers are even strongly stationary by a
careful discussion of the primal first-order conditions of B-stationary type.

25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc