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Any ideas how to solve the following problem:

$Minimize: |F(x,y)|+|G(x,y)|$ s.t. x

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.

1 Answers 1

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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 < A, y < 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 < A, y < B, $z,w \geq 0$

Now, you can solve this using any of the standard techniques.