Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: There is no variational characterization of the cycles in the method of
  periodic projections   The method of periodic projections consists in iterating projections onto $m$
closed convex subsets of a Hilbert space according to a periodic sweeping
strategy. In the presence of $m\geq 3$ sets, a long-standing question going
back to the 1960s is whether the limit cycles obtained by such a process can be
characterized as the minimizers of a certain functional. In this paper we
answer this question in the negative. Projection algorithms that minimize
smooth convex functions over a product of convex sets are also discussed.

12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
18
The categories of this paper are: econ