Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal control of PDEs in a complex space setting; application to the
  Schr\"odinger equation   In this paper we discuss optimality conditions for abstract optimization
problems over complex spaces. We then apply these results to optimal control
problems with a semigroup structure. As an application we detail the case when
the state equation is the Schr\"{o}dinger one, with pointwise constraints on
the "bilinear" control. We derive first and second order optimality conditions
and address in particular the case that the control enters the state equation
and cost function linearly.

36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin