Séminaire de Théorie Algorithmique des Nombres

Witsenhausen's problem asks for the maximum fraction α_n of the n-dimensional unit sphere that can be covered by a measurable set containing no pairs of orthogonal points. We extended well known optimization hierarchies based on the Lovász theta number, like the Lasserre hierarchy, to Witsenhausen's problem and similar problems. We then showed that these hierarchies converge to α_n, and used them to compute the best upper bounds known for α_n in low dimensions.

TBA