Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A unified framework of SAGE and SONC polynomials and its duality theory   We introduce and study a cone which consists of a class of generalized
polynomial functions and which provides a common framework for recent
non-negativity certificates of polynomials in sparse settings. Specifically,
this $\mathcal{S}$-cone generalizes and unifies sums of arithmetic-geometric
mean exponentials (SAGE) and sums of non-negative circuit polynomials (SONC).
We provide a comprehensive characterization of the dual cone of the
$\mathcal{S}$-cone, which even for its specializations provides novel and
projection-free descriptions. As applications of this result, we give an exact
characterization of the extreme rays of the $\mathcal{S}$-cone and thus also of
its specializations, and we provide a subclass of functions for which
non-negativity coincides with membership in the $\mathcal{S}$-cone.
  Moreover, we derive from the duality theory an approximation result of
non-negative univariate polynomials and show that a SONC analogue of Putinar's
Positivstellensatz does not exist even in the univariate case.

0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex