Representations of positive polynomials on noncompact semialgebraic sets via KKT ideals

DOI10.1016/j.jpaa.2006.05.028zbMath1106.13028OpenAlexW2071940220MaRDI QIDQ863907

James W. Demmel, Victoria Powers, Jia-Wang Nie

Publication date: 12 February 2007

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2006.05.028

Mathematics Subject Classification ID

Semidefinite programming (90C22) Sums of squares and representations by other particular quadratic forms (11E25) Semialgebraic sets and related spaces (14P10) Real algebra (13J30)

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Uses Software

• Macaulay2
• Sostools
• SeDuMi
• GloptiPoly

Cites Work

• Minimum ellipsoid bounds for solutions of polynomial systems via sum of squares
• Semidefinite representations for finite varieties
• On the complexity of Putinar's Positivstellensatz
• The \(K\)-moment problem for compact semi-algebraic sets
• Global minimization of a multivariate polynomial using matrix methods
• Semidefinite programming relaxations for semialgebraic problems
• Minimizing polynomials via sum of squares over the gradient ideal
• Complexity estimates for the Schmüdgen Positivstellensatz
• Global Optimization with Polynomials and the Problem of Moments
• Numerical Optimization
• Polynomials Positive on Unbounded Rectangles
• Detecting Global Optimality and Extracting Solutions in GloptiPoly
• Semidefinite Programming
• Ideals, Varieties, and Algorithms
• The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
• Optimization of Polynomials on Compact Semialgebraic Sets
• GloptiPoly
• Semidefinite Approximations for Global Unconstrained Polynomial Optimization
• Introduction to global optimization.
• Computations in algebraic geometry with Macaulay 2
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