Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An exact duality theory for semidefinite programming based on sums of
  squares   Farkas' lemma is a fundamental result from linear programming providing
linear certificates for infeasibility of systems of linear inequalities. In
semidefinite programming, such linear certificates only exist for strongly
infeasible linear matrix inequalities. We provide nonlinear algebraic
certificates for all infeasible linear matrix inequalities in the spirit of
real algebraic geometry: A linear matrix inequality is infeasible if and only
if -1 lies in the quadratic module associated to it. We also present a new
exact duality theory for semidefinite programming, motivated by the real
radical and sums of squares certificates from real algebraic geometry.

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The categories of this paper are: cs
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an