Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new proof for the existence of degree bounds for Putinar's
  Positivstellensatz   Putinar's Positivstellensatz is a central theorem in real algebraic geometry.
It states the following: If you have a set $S= \{ x \in R^n \ | \ g_1 (x) \geq
0, ... , g_m(x) \geq 0\}$ described by some real polynomials $g_i$, then every
real polynomial $f$ that is positive on $S$ can be written as a sum of squares
weighted by the $g_i$ and $1$. Consider such an identity $f= \sum_{i=1}^{m} g_i
s_i + s_0$. For the applications in polynomial optimization, especially
semidefinite programming, the following is important:
  There exists a bound $N$ for the degrees of the $s_i$ which depends only on
the $g_i$, $n$, the degree of $f$, an upper bound for $||f||$ and a lower bound
for $\min f(S)$.
  Two proofs from Prestel and He{\ss} resp. Schweighofer and Nie ([Pr], [He]
resp. [Sw], [NS]) for the existence of these degree bounds are known (also for
the matrix version of Putinar's Positivstellensatz by Helton and Nie [HN]).
Prestel uses valuation and model theory for his approach while Schweighofer
gives a constructive solution by using a theorem of P\'{o}lya.
  In this paper we will give a new elementary, short but non-constructive
proof.

14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
16
The categories of this paper are: stat
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The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th