all,


I met a question that, the cost function of the linear programming problem is a function with absolute value. Here is the problem:
  



min 3x1+|6x2+3|  

st.
|x1+4|+|2x2|<=3
  



How can I deal with it?


Thank you!



Convert linear programming problem into its standard form
Replace $|6 x\_2 + 3|$ by a new variable $x\_3$ with $x\_3 \le 6 x\_2 + 3$ and 
$x\_3 \le -(6 x\_2 + 3)$. Similarly your constraint becomes four constraints 
$\pm (x\_1 + 4) \pm (2 x\_2) \le 3$.


