Global minimization of multivariate polynomials using nonstandard methods

DOI10.1007/s10898-011-9718-xzbMath1275.90096OpenAlexW2117146492MaRDI QIDQ453625

Shuijing Xiao, Guangxing Zeng

Publication date: 27 September 2012

Published in: Journal of Global Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10898-011-9718-x

zbMATH Keywords

global minimumpolynomial optimizationconnected componenttransfer principleinfimuminfinitesimal element

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Nonlinear programming (90C30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Ordered fields (12J15)

Related Items (2)

Equality-constrained minimization of polynomial functions ⋮ Global optimization of polynomials over real algebraic sets

Cites Work

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• Lectures on formally real fields
• On global optimizations with polynomials
• The search for the maximum of a polynomial
• Global minimization of a multivariate polynomial using matrix methods
• An effective decision method for semidefinite polynomials
• Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems
• Computing global minima to polynomial optimization problems using Gröbner bases
• Minimizing polynomials via sum of squares over the gradient ideal
• Algorithms in real algebraic geometry

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