Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nichtnegativstellens\"atze for definable functions in o-minimal
  structures   This paper addresses to Nichtnegativstellens\"atze for definable functions in
o-minimal structures on $(\mathbb{R}, +, \cdot).$ Namely, let $f, g_1, \ldots,
g_l \colon \mathbb{R}^n \to \mathbb{R}$ be definable $C^p$-functions ($p \ge
2$) and assume that $f$ is non-negative on $S := \{x \in \mathbb{R}^n \ | \
g_1(x) \ge 0, \ldots, g_l(x) \ge 0 \}.$ Under some natural hypotheses on zeros
of $f$ in $S,$ we show that $f$ is expressible in the form $f = \phi_0 +
\sum_{i = 1}^l \phi_i g_i,$ where each $\phi_i$ is a sum of squares of
definable $C^{p - 2}$-functions. As a consequence, we derive global optimality
conditions which generalize the Karush--Kuhn--Tucker optimality conditions for
nonlinear optimization.

21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
3
The categories of this paper are: physics
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The categories of this paper are: hep-lat