Trying to understand the example of Chvatal-Gomory cutting planes (Lee p. 153), they say:

$\max 2x_1 + x_2 $
subject to:
$7x_1 + x_2 \leq 28$
$-x_1 +3x_2 \leq 7$
$-8x_1 -9x_2 \leq -32 $
$x_1, x_2 \geq 0$
$x_1, x_2 \in \mathbb{Z}$

The choice of $u_1=0$, $u_2=1/3$, $u_3=1/3$ yields the cutting plane $-3x_1 - 2x_2 \leq -9$. The choice of $u_1 = 1/21$, $u_2=7/22$, $u_3=0$ yields the cutting plane $x_2\leq 3$.

But have no idea how they made that "choice" for the u's! Is it just a guess?

Any tips appreciated!


Yes, it is just a guess. The topic of "how" to choose them is covered later in the book, like in the next chapter.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.