Abstract
Witsenhausen’s problem asks for the maximum fraction αn of the
n-dimensional unit sphere that can be covered by a measurable set containing
no pairs of orthogonal points. The best upper bounds for αn are given by
extensions of the Lov´asz theta number. In this paper, optimization hierarchies
based on the Lov´asz theta number, like the Lasserre hierarchy, are extended to
Witsenhausen’s problem and similar problems. These hierarchies are shown
to converge and are used to compute the best upper bounds for αn in low
dimensions.
n-dimensional unit sphere that can be covered by a measurable set containing
no pairs of orthogonal points. The best upper bounds for αn are given by
extensions of the Lov´asz theta number. In this paper, optimization hierarchies
based on the Lov´asz theta number, like the Lasserre hierarchy, are extended to
Witsenhausen’s problem and similar problems. These hierarchies are shown
to converge and are used to compute the best upper bounds for αn in low
dimensions.
| Original language | English |
|---|---|
| Journal | arXiv preprint |
| Publication status | Published - 2018 |
| Externally published | Yes |