This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x1,..., xn] the ring of polynomials over R in variables x1,..., xn. For an f ∈ R[x1,......This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x1,..., xn] the ring of polynomials over R in variables x1,..., xn. For an f ∈ R[x1,..., xn] and a finite subset H of R[x1,..., xn], denote by V(f : H) the set {f( ˉα) | ˉα∈ Rn, and h( ˉα) =0, ? h ∈ H}. We provide an effective algorithm for computing a finite set U of non-zero univariate polynomials such that the infimum inf V(f : H) of V(f : H) is a root of some polynomial in U whenever inf V(f : H) = ±∞.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.展开更多
In this paper, a new limited memory quasi-Newton method is proposed and developed for solving large-scale linearly equality-constrained nonlinear programming problems. In every iteration, a linear equation subproblem ...In this paper, a new limited memory quasi-Newton method is proposed and developed for solving large-scale linearly equality-constrained nonlinear programming problems. In every iteration, a linear equation subproblem is solved by using the scaled conjugate gradient method. A truncated solution of the subproblem is determined so that computation is decreased. The technique of limited memory is used to update the approximated inverse Hessian matrix of the Lagrangian function. Hence, the new method is able to handle large dense problems. The convergence of the method is analyzed and numerical results are reported.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11161034)
文摘This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x1,..., xn] the ring of polynomials over R in variables x1,..., xn. For an f ∈ R[x1,..., xn] and a finite subset H of R[x1,..., xn], denote by V(f : H) the set {f( ˉα) | ˉα∈ Rn, and h( ˉα) =0, ? h ∈ H}. We provide an effective algorithm for computing a finite set U of non-zero univariate polynomials such that the infimum inf V(f : H) of V(f : H) is a root of some polynomial in U whenever inf V(f : H) = ±∞.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.
基金This research is supported by the National Natural Science Foundation of China, LSEC of CAS in Beijingand Natural Science Foun
文摘In this paper, a new limited memory quasi-Newton method is proposed and developed for solving large-scale linearly equality-constrained nonlinear programming problems. In every iteration, a linear equation subproblem is solved by using the scaled conjugate gradient method. A truncated solution of the subproblem is determined so that computation is decreased. The technique of limited memory is used to update the approximated inverse Hessian matrix of the Lagrangian function. Hence, the new method is able to handle large dense problems. The convergence of the method is analyzed and numerical results are reported.
