Bounds on the infimum of polynomials over a generic semi-algebraic set using asymptotic critical values

Boulos El Hilany, Elias Tsigaridas

We present precise bit and degree estimates for the optimal value of the polynomial optimization problem $f^{\ast }:={\text{inf}}_{x\in \mathcal{X}}f(x)$, where $\mathcal{X}$ is a semi-al…