Positivstellensatz for homogeneous semialgebraic sets
The note contains a complete and elementary proof of a Positivstellensatz for the quadratic module generated by a finite system of homogeneous polynomials. A simple universal denominator and degree bounds are obtained, in the spirit of \textit{B. Reznick} [Math. Z. 220, No. 1, 75--97 (1995; Zbl 0828.12002)]. The result is definitive in its simplicity and will have applications to polynomial optimization.
scientific article; zbMATH DE number 6516544
scientific article