Semidefinite characterization and computation of zero-dimensional real radical ideals
From MaRDI portal
Publication:1029543
DOI10.1007/s10208-007-9004-yzbMath1176.14010arXivmath/0609528OpenAlexW2156811188MaRDI QIDQ1029543
Philipp Rostalski, Monique Laurent, Jean-Bernard Lasserre
Publication date: 13 July 2009
Published in: Foundations of Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0609528
momentsGröbner basessemidefinite programmingeigenvalue methodreal radical idealmoment matricesborder baseszero dimensional ideal
Semidefinite programming (90C22) Numerical computation of solutions to systems of equations (65H10) Real algebraic sets (14P05) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Real algebra (13J30)
Related Items
Local saddle points for unconstrained polynomial optimization, Algebraic criteria of global observability of polynomial systems, Computation with Polynomial Equations and Inequalities Arising in Combinatorial Optimization, Moments and sums of squares for polynomial optimization and related problems, Software for the Gale transform of fewnomial systems and a Descartes rule for fewnomials, Positivity certificates and polynomial optimization on non-compact semialgebraic sets, Certifying the global optimality of quartic minimization over the sphere, Real ideal and the duality of semidefinite programming for polynomial optimization, Tensor eigenvalue complementarity problems, A semidefinite approach for truncated \(K\)-moment problems, Deciding Polyhedrality of Spectrahedra, Homogenization for polynomial optimization with unbounded sets, A hierarchy of spectral relaxations for polynomial optimization, Semidefinite Relaxation Methods for Tensor Absolute Value Equations, VerifyRealRoots: a Matlab package for computing verified real solutions of polynomials systems of equations and inequalities, Distance to a constitutive tensor isotropy stratum by the Lasserre polynomial optimization method, Rational Generalized Nash Equilibrium Problems, Border basis relaxation for polynomial optimization, Computing real radicals and \(S\)-radicals of polynomial systems, Quadratic tensor eigenvalue complementarity problems, Convex generalized Nash equilibrium problems and polynomial optimization, Certifying convergence of Lasserre's hierarchy via flat truncation, Numerically computing real points on algebraic sets, The truncated moment problem via homogenization and flat extensions, A semidefinite method for tensor complementarity problems, On the computation of matrices of traces and radicals of ideals, Design of Marx generators as a structured eigenvalue assignment, Khovanskii-Rolle continuation for real solutions, Semidefinite programming for min-max problems and games, A certificate for semidefinite relaxations in computing positive-dimensional real radical ideals, Lasserre Hierarchy for Large Scale Polynomial Optimization in Real and Complex Variables, Tensor complementarity problems. II: Solution methods, Generators for the \(C^m\)-closures of ideals, The Approach of Moments for Polynomial Equations, Convex Hulls of Algebraic Sets, Stochastic polynomial optimization, A semidefinite programming approach for solving multiobjective linear programming, Linear optimization with cones of moments and nonnegative polynomials, Higher-degree tensor eigenvalue complementarity problems, Test of copositive tensors, A prolongation-projection algorithm for computing the finite real variety of an ideal, Optimization over trace polynomials, A generalized flat extension theorem for moment matrices, Tight relaxations for polynomial optimization and Lagrange multiplier expressions, The maximum tensor complementarity eigenvalues, An SDP relaxation method for Perron pairs of a nonnegative tensor
Uses Software
Cites Work
- Semidefinite representations for finite varieties
- Gröbner bases and primary decomposition of polynomial ideals
- Direct methods for primary decomposition
- Solving zero-dimensional systems through the rational univariate representation
- Radical computations of zero-dimensional ideals and real root counting.
- Aspects of semidefinite programming. Interior point algorithms and selected applications
- Solving polynomial equations. Foundations, algorithms, and applications
- Symmetric Newton polytopes for solving sparse polynomial systems
- Motivations for an arbitrary precision interval arithmetic and the MPFI library
- Global Optimization with Polynomials and the Problem of Moments
- Constructions in Algebra
- Interior Point Trajectories in Semidefinite Programming
- Implementation of interior point methods for mixed semidefinite and second order cone optimization problems
- Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones
- Algorithm 795
- Detecting Global Optimality and Extracting Solutions in GloptiPoly
- Solution of the truncated complex moment problem for flat data
- Semidefinite Programming
- The truncated complex $K$-moment problem
- The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
- Revisiting two theorems of Curto and Fialkow on moment matrices
- A moment approach to analyze zeros of triangular polynomial sets
- Handbook of semidefinite programming. Theory, algorithms, and applications
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item