Computing Rational Points in Convex Semialgebraic Sets and Sum of Squares Decompositions

DOI10.1137/090772459zbMath1279.90127OpenAlexW2064131066MaRDI QIDQ3083312

Lihong Zhi, Mohab Safey El Din

Publication date: 21 March 2011

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://hal.inria.fr/inria-00419983/file/RR-7045.pdf

zbMATH Keywords

complexitysemidefinite programmingconvexrational sum of squares

Mathematics Subject Classification ID

Semidefinite programming (90C22) Positive matrices and their generalizations; cones of matrices (15B48) Quantifier elimination, model completeness, and related topics (03C10) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

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Sum of Squares Decompositions of Polynomials over their Gradient Ideals with Rational Coefficients ⋮ A heuristic method for certifying isolated zeros of polynomial systems ⋮ Certifying solutions to overdetermined and singular polynomial systems over \(\mathbb{Q}\) ⋮ Algorithms for weighted sum of squares decomposition of non-negative univariate polynomials ⋮ Exact algorithms for semidefinite programs with degenerate feasible set ⋮ Bounding averages rigorously using semidefinite programming: mean moments of the Lorenz system ⋮ On exact Reznick, Hilbert-Artin and Putinar's representations ⋮ Sums of squares of polynomials with rational coefficients ⋮ Exact Algorithms for Linear Matrix Inequalities

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