Equality-constrained minimization of polynomial functions

This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x(1),..., x(n)] the ring of polynomials over R in variables x(1),..., x(n). For an f is an element of R[x(1),..., x(n)] and a finite subset H of R[x(1),..., x(n)], denote by nu(f : H) the set {f((alpha) over bar)vertical bar (alpha)over bar> is an element of R-n, and h((alpha)over bar>) = 0, (sic) h is an element of H}. We provide an effective algorithm for computing a finite set U of non-zero univariate polynomials such that the infimum inf nu(f : H) of nu(f : H) is a root of some polynomial in U whenever inf nu(f : H) not equal = +/-infinity. The strategies of this paper are decomposing a finite set of polynomials into triangular chains of polynomials and computing the so-called revised resultants. With the aid of the computer algebraic system Maple, our algorithm has been made into a general program to treat the equality-constrained minimization of polynomials with rational coefficients.