In mathematics, a positive polynomial (respectively non-negative polynomial) on a particular set is a polynomial whose values are positive (respectively non-negative) on that set.
, there exist algebraic descriptions of all polynomials that are positive (resp.
Such a description is a positivstellensatz (resp.
The importance of Positivstellensatz theorems in computation arises from its ability to transform problems of polynomial optimization into semidefinite programming problems, which can be efficiently solved using convex optimization techniques.
[1] Positivstellensatz also exist for signomials,[16] trigonometric polynomials,[17] polynomial matrices,[18] polynomials in free variables,[19] quantum polynomials,[20] and definable functions on o-minimal structures.