Sum of Squares Decompositions of Polynomials over their Gradient Ideals with Rational Coefficients
DOI10.1137/21M1436245OpenAlexW3183238201MaRDI QIDQ5883314
Victor Magron, Trung Vu, Mohab Safey El Din
Publication date: 30 March 2023
Published in: SIAM Journal on Optimization (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2107.11825
Gröbner basisnonnegative polynomialsbit complexitysum of squares decompositiongradient idealzero-dimensional and radical ideal
Sums of squares and representations by other particular quadratic forms (11E25) Real algebraic sets (14P05) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10)
Uses Software
Cites Work
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- Global optimization of polynomials restricted to a smooth variety using sums of squares
- Efficient and accurate computation of upper bounds of approximation errors
- Exact certification in global polynomial optimization via sums-of-squares of rational functions with rational coefficients
- Sums of squares of polynomials with rational coefficients
- Solving systems of polynomial inequalities in subexponential time
- The complexity of partial derivatives
- Solving zero-dimensional systems through the rational univariate representation
- Bit complexity for multi-homogeneous polynomial system solving -- application to polynomial minimization
- Algorithms for weighted sum of squares decomposition of non-negative univariate polynomials
- On exact Reznick, Hilbert-Artin and Putinar's representations
- Intrinsic complexity estimates in polynomial optimization
- On the geometry of polar varieties
- Computing sum of squares decompositions with rational coefficients
- Generalized polar varieties: geometry and algorithms
- There are significantly more nonnegative polynomials than sums of squares
- Minimizing polynomials via sum of squares over the gradient ideal
- Global Optimization with Polynomials and the Problem of Moments
- Exact Algorithms for Linear Matrix Inequalities
- Modern Computer Algebra
- Probabilistic Algorithm for Polynomial Optimization over a Real Algebraic Set
- A proof of the monotone column permanent (MCP) conjecture for dimension 4 via sums-of-squares of rational functions
- Computing Rational Points in Convex Semialgebraic Sets and Sum of Squares Decompositions
- R <scp>eal</scp> c <scp>ertify</scp>
- On Exact Polya and Putinar's Representations
- Real Root Finding for Equivariant Semi-algebraic Systems
- Exact Optimization via Sums of Nonnegative Circuits and Arithmetic-geometric-mean-exponentials
- A second order cone characterization for sums of nonnegative circuits
- Chordal-TSSOS: A Moment-SOS Hierarchy That Exploits Term Sparsity with Chordal Extension
- Exact certification of global optimality of approximate factorizations via rationalizing sums-of-squares with floating point scalars
- Sur la représentation en somme de carrés des polynômes à une indéterminée sur un corps de nombres algébriques
- Convergent SDP‐Relaxations in Polynomial Optimization with Sparsity
- Polar varieties and efficient real elimination
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