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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 of size with rational entries, the set of real vectors such that the matrix $A_0 + x_1 A_1 + \cdots +…