Computing The Equality-Constrained Minimization Of Polynomial Functions In Closed Hypercuboids

Let ? be the field of real numbers, and R[x₁...,,x_n] the ring of polynomials over ? in variables x₁...,,x_n. For an f ∈R[x₁...,,x_n], a finite subset H of R[x₁...,,x_n] and a closed hypercuboid ⁿ∏_i=1[a_i,b_i] in R’ ?n, this paper provides an effective algorithm for computing accurately the minimum of f inZero_R（H）∩ⁿ∏_i=1[a_i,b_i], where Zero_R（H）?is the set of zeros of H in R. Moreover,a minimum point can be created by the algorithm in this paper. With the aid of the computer algebraic system Maple, the algorithm has been compiled into a general program to compute the equality-constrained minimization of polynomials with rational coefficients.