Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergent relaxations of polynomial optimization problems with
  non-commuting variables   We consider optimization problems with polynomial inequality constraints in
non-commuting variables. These non-commuting variables are viewed as bounded
operators on a Hilbert space whose dimension is not fixed and the associated
polynomial inequalities as semidefinite positivity constraints. Such problems
arise naturally in quantum theory and quantum information science. To solve
them, we introduce a hierarchy of semidefinite programming relaxations which
generates a monotone sequence of lower bounds that converges to the optimal
solution. We also introduce a criterion to detect whether the global optimum is
reached at a given relaxation step and show how to extract a global optimizer
from the solution of the corresponding semidefinite programming problem.

34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs