In a previous post, we discussed modeling tricks for min-max problems.  From there, it is simple to handle absolute values as well.  Consider a problem of the form

minimize Abs( a * x + b)

where a is a row vector and x is a column vector.  This problem is equivalent to

minimize max{ a * x + b, - (a * x + b) }

Or, using the trick from the previous post

minimize t

subject to:  a * x + b  <= t

                -(a * x + b) <= t