This has be asked on other forums, though couldn't find authoritative answer.

I have a linear program over the reals and don't want to introduce integer or binary variables.

The objective function is $\text{maximize} \sum |x_i|$ (maximizing sum of absolute values of variables).

Is is possible to model this as a standard linear program (without integer variables and extensions like disjunctions).

What I know. Minimizing sum of absolute values is possible.

This blog suggests several solutions. The solution with SOS2 method appears to work sometimes in glpk and coin-or, though sometimes it doesn't work.

The `lpsolve`

documentation suggests using a binary variable.

If this is impossible, there might be reduction from a NP-hard problem.