Algorithms for computing the global infimum and minimum of a polynomial function

DOI10.1007/s11425-011-4326-2zbMath1260.68486OpenAlexW2257286100MaRDI QIDQ424330

Shuijing Xiao, Guangxing Zeng

Publication date: 31 May 2012

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-011-4326-2

zbMATH Keywords

rational univariate representationglobal minimumpolynomial optimizationtransfer principleinterval representationglobal infimumstrictly critical pointWu's method

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Separable extensions, Galois theory (12F10)

Related Items

Computing polynomial univariate representations of zero-dimensional ideals by Gröbner basis ⋮ Equality-constrained minimization of polynomial functions ⋮ Determination of the limits for multivariate rational functions ⋮ Global optimization of polynomials over real algebraic sets ⋮ Solving the equality-constrained minimization problem of polynomial functions ⋮ Semi-algebraically connected components of minimum points of a polynomial function

Uses Software

• Maple

Cites Work

• Lectures on formally real fields
• The search for the maximum of a polynomial
• On the extension of real places
• Global minimization of a multivariate polynomial using matrix methods
• An effective decision method for semidefinite polynomials
• Computing global minima to polynomial optimization problems using Gröbner bases
• Minimizing polynomials via sum of squares over the gradient ideal
• Global optimization of polynomials using generalized critical values and sums of squares
• Algorithms in real algebraic geometry
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Algorithms for computing the global infimum and minimum of a polynomial function