Simone Naldi

activity

20152020

collaborators

5 papers

cs.SC2020

A divide-and-conquer algorithm for computing Gröbner bases of syzygies in finite dimension

Simone Naldi, Vincent Neiger

Let $f_{1}, \dots, f_{m}$ be elements in a quotient $R^{n} / N$ which has finite dimension as a $K$ -vector space, where $R = K [X_{1}, \dots, X_{r}]$ and $N$ is an $R$ -submodule of $R^{n}$ . We ad…

math.OC2018

Conic programming: infeasibility certificates and projective geometry

Simone Naldi, Rainer Sinn

We revisit facial reduction from the point of view of projective geometry. This leads us to a homogenization strategy in conic programming that eliminates the phenomenon of weak in…

math.AG2018

Spectrahedral representations of plane hyperbolic curves

Mario Kummer, Simone Naldi, Daniel Plaumann

We describe a new method for constructing a spectrahedral representation of the hyperbolicity region of a hyperbolic curve in the real projective plane. As a consequence, we show t…

cs.SC2018

Exact algorithms for semidefinite programs with degenerate feasible set

Didier Henrion, Simone Naldi, Mohab Safey El Din

Given symmetric matrices $A_{0}, A_{1}, \dots, A_{n}$ of size $m$ with rational entries, the set of real vectors $x = (x_{1}, \dots, x_{n})$ such that the matrix $A_0 + x_1 A_1 + \cdots +…

cs.SC2015

Real root finding for rank defects in linear Hankel matrices

Didier Henrion, Simone Naldi, Mohab Safey El Din

Let $H_0, ..., H_n$ be $m \times m$ matrices with entries in $\QQ$ and Hankel structure, i.e. constant skew diagonals. We consider the linear Hankel matrix $H(\vecx)=H\_0+\X\_1H\…