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Results tagged with polynomials
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user 67002
Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.
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Are those two Sum-Of-Squares approach for unconstrained polynomial optimization related?
&\quad p(x)-\lambda = q(x) + \sigma(x) (a-\sum_i x_i^2)\\
&\quad \text{for some SOS polynomials $p$,$\sigma$}\\
&\quad \text{of degree at most $2(\ell+r)$ and $2(\ell+r-1)$, respectively.} … &\quad (1+\sum_i x_i^2)^r \ (p(x)-\lambda) = q(x)\\
&\quad \text{for some SOS polynomials $p$ of degree $2(\ell+r).$}
\end{align}
$$
So my question is: Are these two approaches related / equivalent …
- 617