Codes and Expansions (CodEx) Seminar

Hans Parshall (Western Washington University)
An Approximate Positivstellensatz

In principle, Stengle’s Positivstellensatz can be used to certify that a semialgebraic set is empty via semidefinite programming. Unfortunately, numerical optimization generally fails to deliver an exact Positivstellensatz certificate. As an alternative, we introduce the notion of an approximate Positivstellensatz certificate that promotes numerical approximations of Stengle’s Positivstellensatz certificates to honest certificates. In joint work with Dustin G. Mixon, we found this useful in classifying the optimal packing of 8 points in \( \mathbb{RP}^5 \).