Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonconvex set intersection problems: From projection methods to the
  Newton method for super-regular sets   The problem of finding a point in the intersection of closed sets can be
solved by the method of alternating projections and its variants. It was shown
in earlier papers that for convex sets, the strategy of using quadratic
programming (QP) to project onto the intersection of supporting halfspaces
generated earlier by the projection process can lead to an algorithm that
converges multiple-term superlinearly. The main contributions of this paper are
to show that this strategy can be effective for super-regular sets, which are
structured nonconvex sets introduced by Lewis, Luke and Malick. Manifolds
should be approximated by hyperplanes rather than halfspaces. We prove the
linear convergence of this strategy, followed by proving that superlinear and
quadratic convergence can be obtained when the problem is similar to the
setting of the Newton method. We also show an algorithm that converges at an
arbitrarily fast linear rate if halfspaces from older iterations are used to
construct the QP.

12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg