The problem of minimizing a polynomial function in several variables over ${bf R^n$ is considered and an algorithm is given. When the polynomial has a minimum the algorithm returns the global minimum and finds at least one point in every connected component of the set of minimizers. A characterization of such points is given. When the polynomial does not have a minimum the algorithm can compute its infimum. No assumption is made on the polynomial. The algorithm can be applied for solving a system of polynomial equations.

Nonlinear programming (msc 90C30), Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (msc 13P10)
Life Sciences (theme 5), Energy (theme 4)
CWI
CWI. Probability, Networks and Algorithms [PNA]
Scientific Computing

Hanzon, B, & Jibetean, D. (2001). Global minimization of a multivariate polynomial using matrix methods. CWI. Probability, Networks and Algorithms [PNA]. CWI.