Could you please shed some lights on this? (Not a homework problem)

I am looking for solutions of the following problem in $b$:

$$\max \| X b \|\_2 \quad\text{subject to} \quad \| b - b\_0 \|\_2 < a, \| b \|\_2 = 1$$

where matrix $X$, $a$ and $b\_0$ are given. Is this a *convex* programming problem?

I am thinking of using the Lagrange method to solve it. I am guessing that after I make it into the standard Lagrange form, maybe I could find closed-form solutions? Thank you!