Reflection groups and cones of sums of squares

DOI10.1016/j.jsc.2023.03.001zbMath1521.14102arXiv2011.09997MaRDI QIDQ6108379

Sebastian Debus, Cordian Riener

Publication date: 29 June 2023

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

Full work available at URL: https://arxiv.org/abs/2011.09997

zbMATH Keywords

sums of squaresinvariant theorysymmetry reductionreflection groupspolynomial optimizationreal algebraic geometry

Mathematics Subject Classification ID

Semidefinite programming (90C22) Symmetric functions and generalizations (05E05) Real algebraic and real-analytic geometry (14P99)

Related Items (1)

Linear slices of hyperbolic polynomials and positivity of symmetric polynomial functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Symmetric semi-algebraic sets and non-negativity of symmetric polynomials
• Test sets for nonnegativity of polynomials invariant under a finite reflection group
• On the degree and half-degree principle for symmetric polynomials
• The analogue of Hilbert's 1888 theorem for even symmetric forms
• Symmetry in semidefinite programs
• Even symmetric sextics
• Higher Specht polynomials for the complex reflection group \(G(r,p,n)\)
• An algorithm for sums of squares of real polynomials
• Higher Specht polynomials
• An exact duality theory for semidefinite programming and its complexity implications
• On the positivity of symmetric polynomial functions. I: General results
• Symmetric sums of squares over \(k\)-subset hypercubes
• Projective reflection groups.
• Products of positive forms, linear matrix inequalities, and Hilbert 17th problem for ternary forms
• Symmetry groups, semidefinite programs, and sums of squares
• Real even symmetric ternary forms
• Symmetric ideals, Specht polynomials and solutions to symmetric systems of equations
• New upper bounds for the density of translative packings of three-dimensional convex bodies with tetrahedral symmetry
• There are significantly more nonnegative polynomials than sums of squares
• Symmetric non-negative forms and sums of squares
• Nonnegative polynomials and sums of squares
• Reflection groups, reflection arrangements, and invariant real varieties
• Invariants of Finite Reflection Groups
• Sums of squares and moment problems in equivariant situations
• Invariants of finite groups and their applications to combinatorics
• Spectrahedral Shadows
• Gram spectrahedra
• Symmetry Adapted Gram Spectrahedra
• Exploiting Symmetries in SDP-Relaxations for Polynomial Optimization
• Invariants of Finite Groups Generated by Reflections

This page was built for publication: Reflection groups and cones of sums of squares