Approximating amoebas and coamoebas by sums of squares

DOI10.1090/S0025-5718-2014-02828-7zbMath1318.14054arXiv1101.4114MaRDI QIDQ5497034

Timo de Wolff, Thorsten Theobald

Publication date: 30 January 2015

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.4114

zbMATH Keywords

semidefinite programmingamoebascoamoebasSOS-polynomials, real nullstellensatz

Mathematics Subject Classification ID

Semidefinite programming (90C22) Computational aspects of algebraic surfaces (14Q10) Semialgebraic sets and related spaces (14P10)

Related Items

Degenerations of amoebae and Berkovich spaces, Describing amoebas, Some Recent Developments in Spectrahedral Computation, Amoebas of genus at most one, Computing the connected components of the complement to the amoeba of a polynomial in several complex variables, Amoeba-shaped polyhedral complex of an algebraic hypersurface, Sampling Algebraic Varieties for Sum of Squares Programs, A survey on computational aspects of polynomial amoebas, Metric estimates and membership complexity for Archimedean amoebae and tropical hypersurfaces, Imaginary projections of polynomials, Lopsided approximation of amoebas, Feynman integrals as A-hypergeometric functions, Tropical varieties for exponential sums

Uses Software

• Sostools
• SeDuMi

Cites Work

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• Amoebas of genus at most one
• Discriminant coamoebas in dimension two
• Semidefinite programming relaxations for semialgebraic problems
• Mellin transforms of multivariate rational functions
• Laurent determinants and arrangements of hyperplane amoebas
• A toric positivstellensatz with applications to delay systems
• A nullstellensatz for amoebas
• Global Optimization with Polynomials and the Problem of Moments
• Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones
• Exploiting Algebraic Structure in Sum of Squares Programs
• SOSTOOLS and Its Control Applications
• Hilbert's Nullstellensatz and an Algorithm for Proving Combinatorial Infeasibility
• Computing Amoebas
• Handbook of semidefinite programming. Theory, algorithms, and applications