Computing sum of squares decompositions with rational coefficients

DOI10.1016/j.tcs.2008.09.025zbMath1156.65062OpenAlexW1995320256MaRDI QIDQ2378506

Publication date: 8 January 2009

Published in: Theoretical Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.tcs.2008.09.025

zbMATH Keywords

semidefinite programming algebraic geometry sum of squares symbolic-numerical methods

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Numerical mathematical programming methods (65K05) Nonlinear programming (90C30)

Related Items

Sum of Squares Decompositions of Polynomials over their Gradient Ideals with Rational Coefficients, Inflation of poorly conditioned zeros of systems of analytic functions, Dual Certificates and Efficient Rational Sum-of-Squares Decompositions for Polynomial Optimization over Compact Sets, A heuristic method for certifying isolated zeros of polynomial systems, Sharper and Simpler Nonlinear Interpolants for Program Verification, Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials, Certifying solutions to overdetermined and singular polynomial systems over \(\mathbb{Q}\), Converging outer approximations to global attractors using semidefinite programming, Testing hyperbolicity of real polynomials, Sums of squares in Macaulay2, SONC optimization and exact nonnegativity certificates via second-order cone programming, Convex computation of maximal Lyapunov exponents, A practical approach to SOS relaxations for detecting quantum entanglement, Stability analysis of a bacterial growth model through computer algebra, Pourchet’s theorem in action: decomposing univariate nonnegative polynomials as sums of five squares, Moment ratio inequality of bivariate Gaussian distribution and three-dimensional Gaussian product inequality, On the degree of varieties of sum of squares, Stability analysis of sampled-data control systems with input saturation: a hybrid system approach, Noncommutative nullstellensätze and perfect games, Exact certification in global polynomial optimization via sums-of-squares of rational functions with rational coefficients, Sum-of-Squares Optimization without Semidefinite Programming, Algorithms for weighted sum of squares decomposition of non-negative univariate polynomials, Bounding averages rigorously using semidefinite programming: mean moments of the Lorenz system, Polynomially parameter dependent exponential stabilization of sampled-data LPV systems, An approach to constrained polynomial optimization via nonnegative circuit polynomials and geometric programming, Exact Certification in Global Polynomial Optimization Via Rationalizing Sums-Of-Squares, On the conditions for the finite termination of ADMM and its applications to SOS polynomials feasibility problems, A convex polynomial that is not sos-convex, A method for computing lowest eigenvalues of symmetric polynomial differential operators by semidefinite programming, Vector barrier certificates and comparison systems, Validating numerical semidefinite programming solvers for polynomial invariants, On exact Reznick, Hilbert-Artin and Putinar's representations, Facial reduction for exact polynomial sum of squares decomposition, Equilibrium problems involving the Lorentz cone, On the Generation of Positivstellensatz Witnesses in Degenerate Cases, NCSOStools: a computer algebra system for symbolic and numerical computation with noncommutative polynomials, Exact Semidefinite Programming Bounds for Packing Problems, A linear algebra method to decompose forms whose length is lower than the number of variables into weighted sum of squares, Bounds for Deterministic and Stochastic Dynamical Systems using Sum-of-Squares Optimization, A note on the nonexistence of sum of squares certificates for the Bessis–Moussa–Villani conjecture, Dimension-free entanglement detection in multipartite Werner states, Certified Hermite Matrices from Approximate Roots - Univariate Case, Unnamed Item, Formal Proofs for Nonlinear Optimization, Certification of real inequalities: templates and sums of squares, An algorithm for decomposing a non-negative polynomial as a sum of squares of rational functions

Uses Software

Cites Work