Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Geometry of SDP-Exactness in Quadratic Optimization   Consider the problem of minimizing a quadratic objective subject to quadratic
equations. We study the semialgebraic region of objective functions for which
this problem is solved by its semidefinite relaxation. For the Euclidean
distance problem, this is a bundle of spectrahedral shadows surrounding the
given variety. We characterize the algebraic boundary of this region and we
derive a formula for its degree.

18
The categories of this paper are: econ
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph