A Nonnegative Start of the New Academic Year
Can you put a regular octahedron with one of its vertices in the corner of a rectangular room? And what if this rectangular room is four-dimensional?
Does a given function space possess an orthonormal basis that consists of nonnegative functions (surely this depends on the inner product)?
The Gramian of a matrix with nonnegative entries (trivially) has nonnegative entries and is positive semidefinite. Does the converse hold as well?
We will pay attention to these questions, explain their common features and why they are of interest, at all.
This leads to the introduction of a relatively modern branch of Optimization called Copositive Programming, that formulates certain NP-hard problems as linear optimization problems over convex cones of special matrices. Finally we present a new algorithm for deciding if a matrix belongs to such a cone.
Science Park 107, Room F3.20, or hybrid