4 papers
Exposed extreme rays of the SONC cone
Mareike Dressler, Hongzhi Liao, Vera Roshchina
We provide a complete and explicit characterization of the exposed extreme rays of the cone of sums of nonnegative circuit (SONC) polynomials. The criterion we derive is purely com…
Inner approximations of convex sets and intersections of projectionally exposed cones
Bruno F. Lourenço, Vera Roshchina, James Saunderson
A convex cone is said to be projectionally exposed (p-exposed) if every face arises as a projection of the original cone. It is known that, in dimension at most four, the intersect…
The problem of optimal camouflaging
Alexander Plakhov, Vera Roshchina
We consider the problem of camouflaging for bodies with specular surface in the framework of geometric optics. The index of visibility introduced in [Plakhov 2017] measures the mea…
Douglas--Rachford is the best projection method
Minh N. Dao, Mareike Dressler, Hongzhi Liao +1
We prove that the Douglas--Rachford method applied to two closed convex cones in the Euclidean plane converges in finitely many steps if and only if the set of fixed points of the…