We present a faster interior-point method for optimizing sum-of-squares (SOS) polynomials, which are central tool in polynomial optimization and capture convex programming the Lasserre hierarchy. Let $$p = \sum _i q^2_i$$ be an n-variate SOS of degree 2d. Denoting by $$L:= \left( {\begin{array}{c}n+d\\ d\end{array}}\right) $$ $$U:= {\begin{array}{c}n+2d\\ 2d\end{array}}\right) dimensions vector...

in an earlier work we showed that for ordered fields f not isomorphic to the reals r, there are continuous 1-1 unctions on [0, 1]f which map some interior point to a boundary point of the image (and so are not open). here we show that over closed bounded intervals in the rationals q as well as in all non-archimedean ordered fields of countable cofinality, there are uniformly continuous 1-1 func...