2 citations · 2 across the 3 of their papers we have counts for
8 papers
A Positivstellensatz for Sums of Nonnegative Circuit Polynomials
Mareike Dressler, Sadik Iliman, Timo de Wolff
Recently, the second and the third author developed sums of nonnegative circuit polynomials (SONC) as a new certificate of nonnegativity for real polynomials, which is independent…
An Approach to Constrained Polynomial Optimization via Nonnegative Circuit Polynomials and Geometric Programming
Mareike Dressler, Sadik Iliman, Timo de Wolff
In this article we combine two developments in polynomial optimization. On the one hand, we consider nonnegativity certificates based on sums of nonnegative circuit polynomials, wh…
Gap vectors of real projective varieties
Grigoriy Blekherman, Sadik Iliman, Martina Juhnke-Kubitzke +1
Let be a totally real, non-degenerate, projective variety and let be a generic set of points. Let be the cone of nonnegativ…
Lower Bounds for Polynomials with Simplex Newton Polytopes Based on Geometric Programming
Sadik Iliman, Timo de Wolff
In this article, we propose a geometric programming method in order to compute lower bounds for real polynomials. We provide new sufficient conditions for polynomials to be nonnega…
Amoebas, Nonnegative Polynomials and Sums of Squares Supported on Circuits
Sadik Iliman, Timo de Wolff
We completely characterize sections of the cones of nonnegative polynomials, convex polynomials and sums of squares with polynomials supported on circuits, a genuine class of spars…
Dimensional Differences Between Faces of the Cones of Nonnegative Polynomials and Sums of Squares
Grigoriy Blekherman, Sadik Iliman, Martina Kubitzke
We study dimensions of the faces of the cone of nonnegative polynomials and the cone of sums of squares; we show that there are dimensional differences between corresponding faces…
Low Dimensional Test Sets for Nonnegativity of Even Symmetric Forms
Sadik Iliman, Timo de Wolff
An important theorem by Timofte states that nonnegativity of real -variate symmetric polynomials of degree can be decided at test sets given by all points with at most $\lfl…
Separating inequalities for nonnegative polynomials that are not sums of squares
Sadik Iliman, Timo de Wolff
Ternary sextics and quaternary quartics are the smallest cases where there exist nonnegative polynomials that are not sums of squares (SOS). A complete classification of the differ…