Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of a convex feasibility problem   The 2-sets convex feasibility problem aims at finding a point in the
intersection of two closed convex sets $A$ and $B$ in a normed space $X$. More
generally, we can consider the problem of finding (if possible) two points in
$A$ and $B$, respectively, which minimize the distance between the sets. In the
present paper, we study some stability properties for the convex feasibility
problem: we consider two sequences of sets, each of them converging, with
respect to a suitable notion of set convergence, respectively, to $A$ and $B$.
Under appropriate assumptions on the original problem, we ensure that the
solutions of the perturbed problems converge to a solution of the original
problem. We consider both the finite-dimensional and the infinite-dimensional
case. Moreover, we provide several examples that point out the role of our
assumptions in the obtained results.

27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg