Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal control of a non-smooth quasilinear elliptic equation   This work is concerned with an optimal control problem governed by a
non-smooth quasilinear elliptic equation with a nonlinear coefficient in the
principal part that is locally Lipschitz continuous and directionally but not
G\^ateaux differentiable. This leads to a control-to-state operator that is
directionally but not G\^ateaux differentiable as well. Based on a suitable
regularization scheme, we derive C- and strong stationarity conditions. Under
the additional assumption that the nonlinearity is a PC^1 function with
countably many points of nondifferentiability, we show that both conditions are
equivalent. Furthermore, under this assumption we derive a relaxed optimality
system that is amenable to numerical solution using a semi-smooth Newton
method. This is illustrated by numerical examples.

24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph