A prolongation-projection algorithm for computing the finite real variety of an ideal

DOI10.1016/j.tcs.2009.03.024zbMath1172.14036arXiv0806.3874OpenAlexW2022144677MaRDI QIDQ1029340

Philipp Rostalski, Monique Laurent, Jean-Bernard Lasserre

Publication date: 10 July 2009

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

Full work available at URL: https://arxiv.org/abs/0806.3874

zbMATH Keywords

semidefinite optimizationnumerical algebraic geometryreal solvingfinite real variety

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Semidefinite programming (90C22) Real algebraic sets (14P05) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Real algebra (13J30) Real and complex fields (12D99)

Related Items

Numerically computing real points on algebraic sets, A certificate for semidefinite relaxations in computing positive-dimensional real radical ideals, The Approach of Moments for Polynomial Equations, Linear optimization with cones of moments and nonnegative polynomials, A generalized flat extension theorem for moment matrices, Computing real witness points of positive dimensional polynomial systems

Uses Software

• PHCpack
• SeDuMi
• GloptiPoly
• YALMIP
• ISOLATE

Cites Work

• Semidefinite characterization and computation of zero-dimensional real radical ideals
• Solving zero-dimensional systems through the rational univariate representation
• Aspects of semidefinite programming. Interior point algorithms and selected applications
• Solving polynomial equations. Foundations, algorithms, and applications
• Sparsity in sums of squares of polynomials
• Involutive systems of algebraic equations
• Symmetric Newton polytopes for solving sparse polynomial systems
• Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones
• Algorithm 795
• Detecting Global Optimality and Extracting Solutions in GloptiPoly
• Numerical Polynomial Algebra
• Solution of the truncated complex moment problem for flat data
• Generalized normal forms and polynomial system solving
• The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
• Revisiting two theorems of Curto and Fialkow on moment matrices
• Convergent SDP‐Relaxations in Polynomial Optimization with Sparsity
• Geometry of cuts and metrics
• Algorithms in real algebraic geometry
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