Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Implementation of the ADMM to Parabolic Optimal Control Problems with
  Control Constraints and Beyond   Parabolic optimal control problems with control constraints are generally
challenging, from either theoretical analysis or algorithmic design
perspectives. Conceptually, the well-known alternating direction method of
multipliers (ADMM) can be directly applied to such a problem. An attractive
advantage of this direct ADMM application is that the control constraint can be
untied from the parabolic PDE constraint; these two inherently different
constraints thus can be treated individually in iterations. At each iteration
of the ADMM, the main computation is for solving an unconstrained parabolic
optimal control problem. Because of its high dimensionality after
discretization, the unconstrained parabolic optimal control problem at each
iteration can be solved only inexactly by implementing certain numerical scheme
internally and thus a two-layer nested iterative scheme is required. It then
becomes important to find an easily implementable and efficient inexactness
criterion to execute the internal iterations, and to prove the overall
convergence rigorously for the resulting two-layer nested iterative scheme. To
implement the ADMM efficiently, we propose an inexactness criterion that is
independent of the mesh size of the involved discretization, and it can be
executed automatically with no need to set empirically perceived constant
accuracy a prior. The inexactness criterion turns out to allow us to solve the
resulting unconstrained optimal control problems to medium or even low accuracy
and thus saves computation significantly, yet convergence of the overall
two-layer nested iterative scheme can be still guaranteed rigorously.
Efficiency of this ADMM implementation is promisingly validated by preliminary
numerical results. Our methodology can also be extended to a range of optimal
control problems constrained by other linear PDEs such as elliptic equations
and hyperbolic equations.

23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas