Is it possible to slove problem with norm constraints using only linear programming?

Question

The problem is

$\min_x w^Tx$

s.t. $Ax=b$

$||x||_2=1$

Is there any tricks to handle the norm constraints such that the problem can be solved by only using linear programming tools?

Answer 1

Unless you can get rid of the two-norm, I doubt it's possible.

You can however get it to work with a $||\bullet||_1$ or $||\bullet||_\infty$