Symmetric non-negative forms and sums of squares
G Blekherman, C Riener - Discrete & Computational Geometry, 2021 - Springer
We study symmetric non-negative forms and their relationship with symmetric sums of
squares. For a fixed number of variables n and degree 2 d, symmetric non-negative forms …
squares. For a fixed number of variables n and degree 2 d, symmetric non-negative forms …
[HTML][HTML] Reflection groups and cones of sums of squares
We consider cones of real forms which are sums of squares and invariant under a (finite)
reflection group. Using the representation theory of these groups we are able to use the …
reflection group. Using the representation theory of these groups we are able to use the …
Power mean inequalities and sums of squares
J Acevedo, G Blekherman - Discrete & Computational Geometry, 2024 - Springer
We study the limits of the cones of symmetric nonnegative polynomials and symmetric sums
of squares, when expressed in power-mean or monomial-mean basis. These limits …
of squares, when expressed in power-mean or monomial-mean basis. These limits …
Properly learning poisson binomial distributions in almost polynomial time
I Diakonikolas, DM Kane… - Conference on Learning …, 2016 - proceedings.mlr.press
We give an algorithm for properly learning Poisson binomial distributions. A Poisson
binomial distribution (PBD) of order n∈\mathbbZ_+ is the discrete probability distribution of …
binomial distribution (PBD) of order n∈\mathbbZ_+ is the discrete probability distribution of …
Symmetric nonnegative forms and sums of squares
G Blekherman, C Riener - arXiv preprint arXiv:1205.3102, 2012 - arxiv.org
We study symmetric nonnegative forms and their relationship with symmetric sums of
squares. For a fixed number of variables $ n $ and degree $2 d $, symmetric nonnegative …
squares. For a fixed number of variables $ n $ and degree $2 d $, symmetric nonnegative …
Symmetries in polynomial optimization
This chapter investigates how symmetries can be used to reduce the computational
complexity in polynomial optimization problems. A focus will be specifically given on the …
complexity in polynomial optimization problems. A focus will be specifically given on the …
Extension of Hilbert's 1888 Theorem to Even Symmetric Forms
C Goel - 2014 - kops.uni-konstanz.de
We compare the cone of positive semidefinite (real) forms to its subcone of sum of squares
of (real) forms under the additional assumption of symmetry on the given forms. The aim was …
of (real) forms under the additional assumption of symmetry on the given forms. The aim was …
Nonnegative polynomials and sums of squares: boundary structure, symmetries and sparsity
S Iliman - 2014 - publikationen.ub.uni-frankfurt.de
The cones of nonnegative polynomials and sums of squares arise as central objects in
convex algebraic geometry and have their origin in the seminal work of Hilbert ([Hil88]) …
convex algebraic geometry and have their origin in the seminal work of Hilbert ([Hil88]) …
Low dimensional test sets for nonnegativity of even symmetric forms
S Iliman, T De Wolff - arXiv preprint arXiv:1303.4241, 2013 - arxiv.org
An important theorem by Timofte states that nonnegativity of real $ n $-variate symmetric
polynomials of degree $ d $ can be decided at test sets given by all points with at most …
polynomials of degree $ d $ can be decided at test sets given by all points with at most …
Reflection groups and cones of sums of squares
We consider cones of real forms which are sums of squares and invariant under a (finite)
reflection group. Using the representation theory of these groups we are able to use the …
reflection group. Using the representation theory of these groups we are able to use the …