15 citations · 47 across the 26 of their papers we have counts for
4 papers · 1 filter
Spurious local minima in nonconvex sum-of-squares optimization
Grigoriy Blekherman, Rainer Sinn, Mauricio Velasco +1
We study spurious second-order stationary points and local minima in a nonconvex low-rank formulation of sum-of-squares optimization on a real variety . We reformulate the probl…
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…
Generic Spectrahedral Shadows
Rainer Sinn, Bernd Sturmfels
Spectrahedral shadows are projections of linear sections of the cone of positive semidefinite matrices. We characterize the polynomials that vanish on the boundaries of these conve…
A Note on the Convex Hull of Finitely Many Projections of Spectrahedra
Tim Netzer, Rainer Sinn
A spectrahedron is a set defined by a linear matrix inequality. A projection of a spectrahedron is often called a semidefinitely representable set. We show that the convex hull of…