Lower Bounds for Polynomials with Simplex Newton Polytopes Based on Geometric Programming

DOI10.1137/140962425zbMath1380.12001arXiv1402.6185OpenAlexW2962954083MaRDI QIDQ2805707

Timo de Wolff, Sadik Iliman

Publication date: 13 May 2016

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.6185

zbMATH Keywords

semidefinite programminglower boundsimplexgeometric programmingsparsitysum of squaresnonnegative polynomialsum of nonnegative circuit polynomials

Mathematics Subject Classification ID

Convex programming (90C25) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Real algebraic and real-analytic geometry (14P99)

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Amoebas, nonnegative polynomials and sums of squares supported on circuits ⋮ Initial steps in the classification of maximal mediated sets ⋮ Nonnegative Polynomials and Circuit Polynomials ⋮ Symmetry Reduction in AM/GM-Based Optimization ⋮ SONC optimization and exact nonnegativity certificates via second-order cone programming ⋮ Parameter Region for Multistationarity in \({\boldsymbol{n-}}\)Site Phosphorylation Networks ⋮ Conic linear optimization for computer-assisted proofs. Abstracts from the workshop held April 10--16, 2022 ⋮ Approximating Nonnegative Polynomials via Spectral Sparsification ⋮ An approach to constrained polynomial optimization via nonnegative circuit polynomials and geometric programming ⋮ Real zeros of SONC polynomials ⋮ The dual cone of sums of non-negative circuit polynomials ⋮ Newton polytopes and relative entropy optimization

Uses Software

• GloptiPoly
• POEM

Cites Work

• Amoebas, nonnegative polynomials and sums of squares supported on circuits
• On the computational complexity of membership problems for the completely positive cone and its dual
• Positive semidefinite diagonal minus tail forms are sums of squares
• A tutorial on geometric programming
• Forms derived from the arithmetic-geometric inequality
• Sufficient conditions for a real polynomial to be a sum of squares
• Lower Bounds for Polynomials Using Geometric Programming
• GloptiPoly 3: moments, optimization and semidefinite programming
• Semidefinite Optimization and Convex Algebraic Geometry
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