The Search for the Maximum of a Polynomial

For a real polynomialf(X) ofKvariables the problem of finding maxX Kf(X) is investigated by reducing it to that of searching for the real roots of the univariate polynomial (z): = ∏j(z − f(Λj)), where the product is extended over all the critical points Λjoff(X). Employment of the Hermite method of separation of real solutions of an algebraic equation system permits one to construct along withF(z) its Sturm series, and to restore the coordinates of the corresponding critical point. The problem of finding the max fin the set defined by the real polynomial inequalityG(X) ≥ 0 is also discussed.