Q: Optimization Problem with Modulus function Any ideas how to solve the following problem:
$$Minimize: |F(x,y)|+|G(x,y)|$$ s.t. $x&ltA, y&ltB$
where $$F(x,y)=ax^2+by^2+cx+dy+e$$ $$G(x,y)=fx^2+gy^2+hx+iy+j$$
and $A,B$ are known constants.
Any help would be appreciated.

A: You can modify this program into a QCLP as follows, 
$ Minimize : z + w $ such that $|F(x,y)| \leq z$, $|G(x,y)| \leq w$, $x &lt A$, $y &lt B$, $z,w \geq 0$ 
which basically becomes, 
$ Minimize : z + w $ such that $ -z \leq F(x,y) \leq z$, $-w \leq G(x,y) \leq w$, $x &lt A$, $y &lt B$, $z,w \geq 0$ 
Now, you can solve this using any of the standard techniques.
