Sums of squares in Macaulay2

DOI10.2140/jsag.2020.10.17zbMath1439.13068arXiv1812.05475OpenAlexW3010831251MaRDI QIDQ2184805

Thomas Kahle, Pablo A. Parrilo, Diego Cifuentes

Publication date: 29 May 2020

Published in: The Journal of Software for Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.05475

zbMATH Keywords

sums of squaressemidefinite programming

Mathematics Subject Classification ID

Semidefinite programming (90C22) Software, source code, etc. for problems pertaining to commutative algebra (13-04) Real algebra (13J30) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

Related Items (8)

Matroids on Eight Elements with the Half-Plane Property and Related Concepts ⋮ Moment ratio inequality of bivariate Gaussian distribution and three-dimensional Gaussian product inequality ⋮ Nonlinear algebra and applications ⋮ Identifiability in Continuous Lyapunov Models ⋮ Bad projections of the PSD cone ⋮ SumsOfSquares ⋮ Exact Semidefinite Programming Bounds for Packing Problems ⋮ Convex Algebraic Geometry of Curvature Operators

Uses Software

• CSDP
• Macaulay2
• SDPA
• Mosek

Cites Work

• Products of positive forms, linear matrix inequalities, and Hilbert 17th problem for ternary forms
• Computing sum of squares decompositions with rational coefficients
• CSDP, A C library for semidefinite programming
• Implementation and evaluation of SDPA 6.0 (Semidefinite Programming Algorithm 6.0)
• Exploiting Algebraic Structure in Sum of Squares Programs
• Semidefinite Optimization and Convex Algebraic Geometry

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