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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!

2 Answers 2