I wish to know if there is a closed form solution of a program of the following form
$\max_w x^Tw \text{ such that } \tau_2\| w \|_2 + \tau_1 \| w \|_1 \leq 1, ~\ \tau_1, \tau_2 > 0$
When either of the $\tau$ are zero, we can obtain a closed form solution. I am unable to obtain one for arbitrary $\tau$ though. The constraint set is a ball that looks similar to the "elastic net" penalty in statistics.