How can I solve a problem such as the following:
$$ \text{minimize}~~~ \sum_{i=1}^n |x_i| \\ \text{subject to}~~~ A x \geq b $$ ? Without the absolute values on the variables, it is a simple linear program. Is it possible to convert the verstion with absolute values into a standard linear program?
Note: this question How to minimize an absolute value in the objective of an LP? looks similar, but it is different.