TITLE: Maximal norm-1 projection
QUESTION [5 upvotes]: Suppose I have a real unitary matrix $U$ and a unit vector $\mathbf{x}, \|\mathbf{x}\|_2 = 1$. What is the solution to the following problem?
$$
\widehat{\mathbf{x}} = \arg\max_{\mathbf{x}, ~\|\mathbf{x}\|_2 = 1}\|U\mathbf{x}\|_1.
$$

REPLY [2 votes]: The following may be of interest: K. Drakakis, "On the calculation of the l2 -> l1
induced matrix norm", Int. J. Algebra, 2009 (3), No 5, 231-240 (pdf).