82 citations · 169 across the 34 of their papers we have counts for
6 papers · 1 filter
A semidefinite programming hierarchy for covering problems in discrete geometry
Cordian Riener, Jan Rolfes, Frank Vallentin
In this paper we present a new semidefinite programming hierarchy for covering problems in compact metric spaces. Over the last years, these kind of hierarchies were developed prim…
Symmetric SAGE and SONC forms, exactness and quantitative gaps
Philippe Moustrou, Cordian Riener, Thorsten Theobald +1
The classes of sums of arithmetic-geometric exponentials (SAGE) and of sums of nonnegative circuit polynomials (SONC) provide nonnegativity certificates which are based on the ineq…
Faster real root decision algorithm for symmetric polynomials
George Labahn, Cordian Riener, Mohab Safey El Din +2
In this paper, we consider the problem of deciding the existence of real solutions to a system of polynomial equations having real coefficients, and which are invariant under the a…
Symmetries in polynomial optimization
Philippe Moustrou, Cordian Riener, Hugues Verdure
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 Moment-SO…
Optimization of trigonometric polynomials with crystallographic symmetry and spectral bounds for set avoiding graphs
Evelyne Hubert, Tobias Metzlaff, Philippe Moustrou +1
Trigonometric polynomials are usually defined on the lattice of integers.We consider the larger class of weight and root lattices with crystallographic symmetry.This article gives…
The Wonderful Geometry of the Vandermonde map
Jose Acevedo, Grigoriy Blekherman, Sebastian Debus +1
We study the geometry of the image of the nonnegative orthant under the power-sum map and the elementary symmetric polynomials map. After analyzing the image in finitely many varia…