Converting absolute value program into linear program I have the generic optimization problem:
$$ \max c^T|x|$$
$$ \text{s.t. } Ax \le b $$
$x$ is unrestricted
How do I convert it into a linear programming problem? 
Online I read something about letting $x$ equal the difference of 2 positive numbers but I could not intuitively grasp why that worked. Plus the example applied only to minimization problems where the $c^T$ entries are all greater than $0$.
I'm sort of stuck

I realize this is old, but I just ran into this issue. Please see: http://lpsolve.sourceforge.net/5.1/absolute.htm, which has a great explanation of the solution (both for minimization and maximization of an absolute value), and helped me a lot. 
